Which statement describes if there is an extraneous solution to the equation √x-3 = x-5? A. there are no solutions to the equation, B. the extraneous solution is x = 7, C. the valid solutions are x = 7 and x = 4, or D. the extraneous solution is x = 4
Answers
Lets solve our equation to find out what is the extraneous solution:
[tex] \sqrt{x-3} =x-5[/tex]
[tex](\sqrt{x-3})^2 =(x-5)^2[/tex]
[tex]x-3=x^2-10x+25[/tex]
[tex]x^2-11x+28=0[/tex]
[tex](x-4)(x-7)=0[/tex]
[tex]x-4=0[/tex] and [tex]x-7=0[/tex]
[tex]x=4[/tex] and [tex]x=7[/tex]
So, the solutions of our equation are [tex]x=4[/tex] and [tex]x=7[/tex]. Lets replace each solution in our original equation to check if they are valid solutions:
- For [tex]x=7[/tex]
[tex] \sqrt{x-3} =x-5[/tex]
[tex]\sqrt{7-3} =7-5[/tex]
[tex] \sqrt{4} =2[/tex]
[tex]2=2[/tex]
We can conclude that 7 is a valid solution of the equation.
- For [tex]x=4[/tex]
[tex] \sqrt{x-3} =x-5[/tex]
[tex]\sqrt{4-3} =4-5[/tex]
[tex] \sqrt{1} =1[/tex]
[tex]1 \neq 1[/tex]
We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.
We can conclude that the correct answer is: D. the extraneous solution is x = 4
Answer:
D. the extraneous solution is x = 4
Step-by-step explanation:
You want to know the statement that describes if there is an extraneous solution to the equation √x-3 = x-5.
SolutionA straightforward (blind) solution to the problem proceeds by squaring both sides and solving the quadratic:
x -3 = x² -10x +25
x² -11x +28 = 0
(x -7)(x -4) = 0 ⇒ x = 4 or x = 7
When you try these solutions in the original equation, you get ...
√(4 -3) = 4 -5 ⇒ 1 = -1 . . . . . x = 4 is an extraneous solution, choice D
√(7 -3) = 7 -5 ⇒ 2 = 2 . . . . . x = 7 is the solution
DomainThe square root function is only defined for non-negative values, so the left side of the equation is only defined for x ≥ 3.
The left side of the equation produces non-negative values. The right side of the equation will have non-negative values only for x ≥ 5.
Considering the domain of the equation is x ≥ 5, we know that x = 4 cannot be a solution. It can be ignored. This value only arises because squaring the radical allows values of x that require the root to be negative.
__
Additional comment
The attached graph shows the only solution is x=7, the value that makes the difference between the sides of the equation be zero. We find it useful to write radical equations in the form f(x) = 0, making the x-intercepts of the graph of f(x) be the solution(s). The graphing calculator does not graph the function where it is undefined, so the domain restrictions are automatically accommodated.
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If the sum of three numbers is 144, what is the average of the three numbers?
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Lisa arranges six square paintings as shown in the area of the arrangement is 225 cm² what would it cost Lisa to frame her arrangement at a cost of $.12 per centimeter
Answers
To frame Lisa's arrangement of six square paintings, the total cost would be $43.20.
Explanation:To find the cost of framing Lisa's arrangement, we need to calculate the perimeter of the arrangement and then multiply it by the cost per centimeter. Since the arrangement consists of six square paintings, we can calculate the side length of one square by taking the square root of the total area of 225 cm². The side length of one square is 15 cm, so the perimeter of one square is 4 multiplied by 15 cm, which is 60 cm. Since there are six squares, the total perimeter of the arrangement is 6 multiplied by 60 cm, which is 360 cm. Finally, we multiply the total perimeter by the cost per centimeter of $.12 to find the total cost of framing, which is 360 cm multiplied by $0.12, equaling $43.20.
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draw an angle measuring 700 degrees in standard position.
Answers
700 is almost 2 complete revolutions around the graph. 700-360=340; this means it is the same as going 20° backwards from the starting point.
What is the associative property
Answers
Example 1:
1 + 2 + 3
We can solve this by first doing 1 + 2 = 3, and then adding 3 + 3 = 6. OR we can start with 2 + 3 = 5, and add 5 + 1 = 6. We can even do, 3 + 1 = 4, then add 4 + 2 = 6. Either way, we end up with the same correct answer.
Example 2:
1 x 2 x 3
Same thing applies to multiplication. We can start by doing 1 x 2 = 2, and then 2 x 3 = 6. OR we can do 2 x 3 = 6, then 6 x 1 = 6. Just like the one above, we can also do, 3 x 1 = 3, then 3 x 2 = 6. Either way you group them, you get the same answer.
Example 3:
- 1 - 2 - 3
We can do - 1 - 2 = - 3, then - 3 - 3 = - 6. OR - 1 - 3 = - 4, then - 4 - 2 = - 6. OR - 2 - 3 = - 5, then - 5 - 1 = - 6. Again, same answer, three different ways to group it.
THIS DOES NOT WORK WHEN THE ADDITION/SUBTRACTION and MULTIPLICATION OPERATIONS ARE IN THE SAME PROBLEM
If given 1 + 3 - 7 x 4, you cannot rearrange the components like you can with the associative property. You will end up with drastically different answer when there is only one way to do this.
Here is an incorrect example of it.
1 + 3 + 7 x 4
1 + 10 x 4
11 x 4
44.
That is wrong. The correct way is
1 + 3 + 7 x 4
1 + 3 + 28
Now because all of the operations match you can use associative property to arrive at the same answer the three different ways.
4 + 28 = 32. OR 1 + 31 = 32. OR 29 + 3 = 32. See the difference in the answers?
simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39)
Answers
[tex]5.23x + 3.76 - 3.67x + 6.39 \\ = 1.56x + 10.15[/tex]
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
Three out of four student surveyed in a school said they will vote for nuncio for class president. Predict how many of the 340 students in the school would vote for nuncio?
Answers
write it out:
.75*340
solve:
255
about 255 students are likely to vote for Nuncio
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Answers
The perimeter is L + w + L + perimeter of a semicircle.
L = 22 cm
W = 18 cm
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pi * r
r = 18/2 = 9 or
r = 22/2 = 11
So the perimeter of the semi circle is pi * 9 = 25.12 The total Perimeter = 22 + 22 + 18 + 25.12 = 87.12
It can also be 22 + 18 + 22 + 34.54 = 96.54 There are even more possiblities for perimeter. I would have the same problem if you asked about area.
Why not put more details in and I'l give you the correct answer. Here is what we need to know
1. Where is the circle on the 22 cm side or the 18 cm side?
2. What are you looking for: perimeter or area? As soon as you answer these I'll be back.
A recipe for cookies requires 2/3 cup of butter. Rama wants to make 3/4 of the recipe. How many cups of butter should Rama use to make the cookies?
Answers
= (2/3)(3/4)
multiply numerators; multiply denominators
= (2*3)/(3*4)
= 6/12
simplify by 6
= 1/2 cup
ANSWER: Rama should use 1/2 cup of butter.
Hope this helps! :)
Y = 2x - 1 and y = x + 3 find the solution by graphing or substitution
1. ( 4,7)
2. ( 7,4)
3. ( -7,-4)
4. Infinite solutions
Answers
Answer:
Ripboodap9urmy you are wrong utterly wrong. I had a feeling you were guessing why would you say it's the third choice out of the blue
Step-by-step explanation:
And person who's asking this believe me it is (4,7) I ligit just took the test and got it correct and it's the first choice.
Plzz give me brainlist!!
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Answers
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---------------------------
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What is the equation for the sum of three consecutive even numbers totaling 198.
Question 4 options:
n+n+1+n+2=198
n+n+2+n+4=198
3n=198
n+3=198
Answers
Final answer:
Option B: n+n+2+n+4=198
The equation for the sum of three consecutive even numbers totaling 198 can be represented as
n + (n+2) + (n+4) = 198,
where n is the first even number.
Solving the equation, the first even number is 64, and the consecutive even numbers are 66 and 68.
Explanation:
The equation for the sum of three consecutive even numbers can be represented as n + (n+2) + (n+4) = 198, where 'n' is the first even number. Let's solve the equation:
Combine like terms: 3n + 6 = 198Subtract 6 from both sides: 3n = 192Divide both sides by 3: n = 64So, the first even number is 64, and the consecutive even numbers are 66 and 68.
∠YXZ and ∠ZXW are adjacent and supplementary angles. If m∠YXZ = 37°, what is m∠ZXW?
A. 143°
B. 37°
C. 53°
D. unknown
Answers
To get this answer quickly, you subtract the given angle (37) from 180 to get 180-37 = 143
The more longer answer would look something like this
x+37 = 180 .... the two supplementary angles add to 180 degrees
x+37-37 = 180-37 .... subtract 37 from both sides
x+0 = 143
x = 143
where x is the measure of angle ZXW
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How much more fertilizer should each bucket get?
A. 1/9 of a pound
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Answer:
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Step-by-step explanation:
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V=s*s*s
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He counted 206 wheels and 170 pedals. How many bicycles and tricycles does he have.
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tricycle has 3 wheels and 2 pedals
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subtract EQ 1 from EQ 2
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The diameter of the large circle = 3 diameters of the small circle.
The radius of the large circle = 3 radii of the small circles.
Step one
Find the radius of the large circle.
r_small = 5 cm Given
r_large = 5 * 3 cm Construction
r_large = 15 cm
Step Two
Find the Area of the large circle
Area = pi * r^2
Area = 3.14 * 15^2
Area = 3.14 * 225
Area = 706.5.
Step Three
Find the area of the 7 small circles.
r = 5 cm given
pi = 3.14
Area = 3.14 * 5^2
Area = 3.14 * 25
Area = 78.5 cm^2
Area of 1 circle = 78.5 cm^2
Area of 7 circles = x Cross multiply
x * 1 = 78.5 cm^2 * 7
x = 549.5 cm^2
Step four
Find the area of the 6 congruent shapes (one of which is shaded).
Area of the six congruent shapes = area of the large circle - area 7 small circles.
Area of seven large circle = 706.5 cm^2
Area of 7 small circles = 549.5 cm^2 Subtract
Area of 6 congruent shapes 157 cm^2
Step 5
Find the area of the shaded area
6 congruent shapes = 157 cm^2 Cross multiply
1 shaded = x
6x = 1 * 157 Divide by 6
x = 157 / 6
x = 26.166667 cm^2 <<<<<<<<<<< answer
If your answer is in terms of pi then the answer us
X = 50 pi / 6 or 25 pi / 3 Alternate possibilities.
Susan received grades of 78, 93, 82, and 76 on four math exams. What is the lowest score she can receive on her next math exam and have an average of at least 85 on the five exams?
A) 96
B) 94
C) 92
D) 90
E) 88
Answers
Choice A) 96
==========================================
Explanation:
The original list of scores is {78, 93, 82, 76}
Add x to the list to get this new list {78, 93, 82, 76, x}
Let's find the average of the new set
Add up the values and divide by 5. We force this average to be 85 since this is the grade Susan wants
(78+93+82+76+x)/5 = 85
(329+x)/5 = 85
329+x = 85*5
329+x = 425
x = 425-329
x = 96
So if Susan gets a 96 or greater on the fifth test, then she'll have an average of at least 85 (that score or greater)
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Use the expression 4(8 + 3x) to answer the following:
Part A: Describe the two factors in this expression.
Part B: How many terms are in each factor of this expression?
Part C: What is the coefficient of the variable term?
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https://brainly.com/question/9954194
The expression 4(8 + 3x) has two factors: the number 4 and the binomial (8 + 3x). The number 4 has one term, and the binomial has two terms (8 and 3x). The coefficient of the variable term 3x is 3.
In response to the question about using the expression 4(8 + 3x), let's break it down.
Part A: Describe the two factors in this expression.
The expression has two factors: the numeral 4 and the parenthetical (8 + 3x).
Part B: How many terms are in each factor of this expression?
The first factor, 4, consists of one term because it is a single number. The second factor, (8 + 3x), consists of two terms: the constant term 8, and the variable term 3x.
Part C: What is the coefficient of the variable term?
The coefficient of the variable term 3x is 3.
Native Americans once lived near Cartersville, Georgia, in an area that is now a state park. They constructed burial mounds that often contained artifacts, such as beads, feathers, and copper ear ornaments. One of the park's mounds is 63 feet in height. Be a Math Detective. If the top of the mound is rectangular in shape with a perimeter of 322 yards, what could be the side lengths of the rectangle?
Answers
The sides of the rectangle atop of the mound could be multiple pairs of measurements. One such possible example is 100 yards by 61 yards which satisfy the perimeter equation, given the perimeter of the rectangle is 322 yards.
Explanation:The question is asking about the side lengths of the rectangular top of an ancient mound in Cartersville, Georgia. This is a math problem that uses the concept of perimeter.
The perimeter of a rectangle is given by the formula: P = 2l + 2w where P is the perimeter, l is the length, and w is the width. We know that the perimeter of the rectangle is 322 yards. We can solve for the sides (length and width) by setting up equations using various combinations of numbers that, when plugged into the formula, result in a sum of 322.
It's important to note that we won't have a unique solution to this because a rectangle's perimeter doesn't determine its side lengths uniquely, but only within certain limits. So, there could be multiple correct answers.
For example, if we consider the length to be 161 yards, and the width to be 0 yards, it would still satisfy the perimeter equation. But since width cannot be zero, we can suppose the length to be longer side and width to be smaller, say 100 yards and 61 yards, which also add up to produce a perimeter of 322 yards. So, one possible solution is 100 yards by 61 yards.
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write the equation 12=3x + 6 in the form ax + b = c with c=12 what are the values of a & b?
Answers
is effectively c=ax+b
meaning
a is 3
b is 6 and
c is 12
[tex]ax + b = c \\ 3x + 6 = 12[/tex]
Answer : a = 3, b = 6
Hope this helps. - M
what is produced in photosynthesis
Answers
Hope this helps!
Answer:
The answer is oxygen and glucose
Step-by-step explanation:
Science man
rectangle A is 15cm long. rectangle B is 40cm long and its width is 8 less than rectangle A. The area of Rectangle B is double Rectangle A. what is the width of Rectangle B?
Answers
You can get this by setting the rectangle A width to x and the rectangle B width to x - 24. Then set the area of A multiplied by 2 equal to the area of B. You can then solve for x.
The height of a model rocket is 4.5% of the height of the actual rocket. The model is 1.32m high. How high is the actual rocket? Please show your work.
Answers
x is the actual height of the rocket.
4.5% is really 0.045 (move the decimal place 2 times to the left).
1.32 = 0.045x
Divide both sides by 0.045.
x = 29.3
The height of the actual rocket is 29.3 meters.
To find the height of the actual rocket given the height of the model rocket, we can use the ratio between the two. By setting up and solving a simple equation, we can determine that the height of the actual rocket is 29.33 meters.
To find the height of the actual rocket, we need to start by determining the ratio between the height of the model rocket and the actual rocket. Given that the model rocket is 4.5% of the height of the actual rocket, we can use this ratio to solve for the height of the actual rocket.
Let's denote the height of the actual rocket as x. Since the model rocket is 4.5% (or 0.045) of the actual rocket's height, we can set up the equation:
0.045x = 1.32
To solve for x, we divide both sides of the equation by 0.045:
x = 1.32 / 0.045
Calculating this expression gives us the height of the actual rocket as 29.33 meters.
Which of the following functions are quadratic functions? (Select all that apply.)
A.f(x) = 2x − 4
B.f(x) = 3 − x2
C.f(x) = 3x2 − x − 6
D.f(x) = 3 x2
Answers
(ax2+bx+c)
Which is an equation of the given line in standard form?
A. -6x+5y=13
B. -6x+7y=-11
C. -6x+7y=11
D. -7x+6y=-11
Answers
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The coordinates of the points:
[tex](-3;\ -1)\to x_1=-3;\ y_1=-1;\ \left(\dfrac{1}{2};\ 2\right)\to x_2=\dfrac{1}{2};\ y_2=2[/tex]
Substitute:
[tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}[/tex]
We have:
[tex]y=\dfrac{6}{7}x+b[/tex]
Substitute the coordinates of the point (-3; -1) to the equation of the line:
[tex]-1=\dfrac{6}{7}\cdot(-3)+b\\\\-1=-\dfrac{18}{7}+b\ \ \ |+\dfrac{18}{7}\\\\b=\dfrac{11}{7}[/tex]
Therefore we have:
[tex]y=\dfrac{6}{7}x+\dfrac{11}{7}\ \ \ |\cdot7\\\\7y=6x+11\ \ \ |-6x\\\\\boxed{-6x+7y=11}[/tex]
Answer: C. -6x + 7y = 11