Answer:
2
Step-by-step explanation:
Its an extraneous solution, not a normal solution. It shouldn't be -4, it should be 2.
The extraneous solution obtained by Kaylee is y = 4.
To solve the equation, let's follow Kaylee's approach and square both sides:
[tex](1 - y)^2 = (2y^2 - 7)[/tex]
Expanding the left side:
[tex]1 - 2y + y^2 = 2y^2 - 7[/tex]
Rearranging the equation and combining like terms:
[tex]y^2 - 2y^2 + 2y - 1 - 7 = 0\\\\-y^2 + 2y - 8 = 0[/tex]
Now, to solve this quadratic equation, we can factor it:
-(y - 4)(y + 2) = 0
Setting each factor equal to zero:
y - 4 = 0 or y + 2 = 0
Solving for y in each equation:
y = 4 or y = -2
However, we need to check if these solutions are extraneous by substituting them back into the original equation:
For y = 4:
[tex]1 - 4 = \sqrt{2(4^2) - 7}\\\\-3 = \sqrt{32 - 7}\\\\-3 = \sqrt{25}[/tex]
-3 ≠ 5
For y = -2:
[tex]1 - (-2) = \sqrt{2(-2^2) - 7}\\\\3 = \sqrt{8 - 7}\\\\3 = 1[/tex]
From the above analysis, we see that when y = 4, it leads to an extraneous solution, as it does not satisfy the original equation.
Therefore, the extraneous solution obtained by Kaylee is y = 4.
To know more about extraneous solution, refer here:
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Could someone help what is the variable in “8y3”?
Answer:
y
Step-by-step explanation:
The variable in 8y^3 is y because a variable is a number that we don't know yet, and that is the only one.
1. Which region has the highest population?
2. Which region has the lowest population?
3. Which range (in millions of people) on the chart contains
the greatest number of regions; 0-3, 3-6, 6-9, 9-12, 12-15 or 15-18?
4. Which regions contain more than 3 million males?
5. Does any region have significantly more females to males
in it?
6. What is the difference (to the nearest million) between the
biggest populated region and the next biggest populated
region?
all I know is for #2 greenland
HELP EASY PHYSICS QUESTION URGENT :))
A ball is kicked off the ground with a velocity of 15 m/s at an angle of 30° horizontally. What is the horizontal distance the ball travels before returning to the ground?
a.15.5 m
b.17.5 m
c.19.5 m
d.21.5 m
Answer:
The horizontal distance the ball travels before returning to the ground is 19.5 m
Step-by-step explanation:
Formula of range of horizontal distance =[tex]\frac{u^2 Sin 2 \theta}{g}[/tex]
Where u is the initial velocity
g is gravity
We are given that A ball is kicked off the ground with a velocity of 15 m/s at an angle of 30° horizontally.
So, u = 15 m/s
[tex]\theta = 30^{\circ}[/tex]
g = 10
So, the horizontal distance the ball travels before returning to the ground = [tex]\frac{15^2 Sin 2(30^{\circ})}{10}=19.48 \sim 19.5 m[/tex]
Hence The horizontal distance the ball travels before returning to the ground is 19.5 m
Which graph represents the function h(x) = [X1 +0.5?
12
V
2
1
2
-2
Answer:
Actually, if you graph it the correct answer is the third option, not the first
Trust me I got 100%
Find the 7th term of the geometric sequence a3 =128,r=-1/4
Answer:
Step-by-step explanation:
The general formula for this sequence is a(n) = a(1)*(-1/4)^(n - 1). We don't yet know a(1).
If a(3) = 128, then 128 = a(1)*(-1/4)^(3 - 1), or
128 = a(1)*(1/16)
and so a(1) = 128/16
resulting in the specific formua a(n) = 8(-1/4)^(n - 1)
Now let's find a(7):
a(7) = 8(-1/4)^1 * (-1/4)^(6)
or
a(7) = 8(-1/4)^7
What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1
Answer:
Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (… ... Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1 ... To get the sum to infinity of the geometric series, we need to get its first term
Step-by-step explanation:
Please help me with 1 more question ill give good ratings please!
Answer:
(4, - 4 )
Step-by-step explanation:
Since the dilatation is centred at the origin, multiply the original coordinates by the scale factor, that is
(1, - 1 ) → (4(1), 4(- 1)) → (4, - 4 )
63 people are going to the zoo. There are 3 cars to take people to the zoo. How
many will go in each car if the same number go in each car?
Answer:
21
3x21= 63 have a great day
Step-by-step explanation:
BRAINLIEST PLEASE
Consider the diagram. Parallel lines r and s are cut by transversal q. On line r where it intersects line q, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line s where it intersects line q, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. Given that r||s and q is a transversal, we know that by the [________]. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
Answer:
alternet interior angles i think?
Step-by-step explanation:
Angles between transversal of parallel lines are related by several angle theorems.
The theorem that supports r || s and transversal q is (b) alternate interior angles theorem
From the image of lines q, r and s (see attachment), we have the following highlights.
Angles 3 and 6; angles 4 and 5, are alternate interior angles, and they are congruent
The above means that:
Angles 2 and 7; angles 1 and 8, are also congruent
Hence, r || s and q is a transversal, because of the alternate interior angle theorem.
Read more about parallel lines and transversal at:
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Answer the statistical measures and create a box and whiskers plot for the following set of data. You may optionally click and drag the numbers into numerical order.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
3,4,5,6,6,7,7,12,13,14,14,15,15,16,17
Min:
Q1:
Med:
Q3:
Max:
For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
What is box and whiskers plot?
Box and wishkers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.
The minimum and the maximum values in the box plot is plotted at the end points.
The following set of data which i s given in the problem.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
Min: 3The minimum value in the given data is 3. Thus, the min is 3.
Q1:6First quartile appears at 6. Thus, the value of Q1 is 6.
Med:12The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.
Q3:14.5Second quartile appears at 14.5. Thus, the value of second quartile Q2 is 6.
Max: 17The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.
Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
Learn more about the box and whiskers plot here;
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t - 10 + t = 40 what is the value of t
Answer:
t = 25
Step-by-step explanation:
t - 10 + t = 40
2t = 40+10
2t = 50
t = 50/2
t = 25
Hope this helps.
Answer:
Step-by-step explanation:
Can someone please help!!
Answer:
let’s find the area of the circle first.
The formula to find the area of the circle is 3.14 x r^2
3.14 x 0.5^2 = 0.785 cm^2
Lets find the area of the triangle.
the formula to find the area of the triangle is 1/2 x base x height
The height is found if you subtract the square of 5 from the square of 4.
5^2 - 4^2 = 9
the square root of 9 is 3.
1/2 x 8 x 3 = 12 cm^2
lets find the area of the rectangle
length x width
8 x 4.5 = 36 cm^2
then subtract the area of the circle from the area of the rectangle and then add the area of the triangle
36 - 0.785 + 12 = 47.215 (round it off to 47)
If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost?
Question 10 options:
a)
$37.75
b)
$29.75
c)
$0.16
d)
$47.60
The diameter of a circle is 5ft. Find the circumference to the nearest tenth
Answer:
Answer is 16 ft.
The answer is rounded to the nearest tenth place.
Step-by-step explanation:
[tex]given \: that \: \\ diameter \: of \: circle \: = 5 \: ft \\ then \: radius \: = \frac{5}{2} \: ft \\ we \: know \: that \\ circumferece = 2\pi \: r \\ on \: substiuting \: r= \frac{5}{2} \: ft \ \\ in \: formula \\ circumferece = 2\pi \times \frac{5}{2} \\ = 5\pi \\ substiuting \: \pi = 3.14 \\ = 5(3.14) \\ = 15.7079 \\ = 15.708 \\ when \: it \: is \: rounded \: off \: to \: nearest \: tenth \\ we \: get \: 16 \: ft\: as \: the \: answer.[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
The circumference of the circle having a diameter of 5 ft will be 15.7 ft.
What is circumference?
The easiest way to find the perimeter for any shape is to add up the lengths of all the sides, but a circle only has one side, so that isn't possible. If you don't know its circumference, you also don't know the length of that side.
Fortunately, we can use a formula that uses other properties of a circle to find its circumference. In fact, there are two different formulas for circumference we can use and they look like this:
C = 2πr
Here the diameter of the giver circle is 5 ft so the radii will be 2.5 ft
By putting the value of radius in the formula we get
[tex]C=2\pi r[/tex]
[tex]C=2\pi \times 2.5=15.7\ ft[/tex]
Hence the circumference of the circle having a diameter of 5 ft will be 15.7 ft.
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please come in clutch and help me please and thank you!
Answer:
3/20
Step-by-step explanation:
its 3/20 because its really the only possible answer that has 20 has its denominator
Help. Will mark brainiest
Answer:
Step-by-step explanation:
The third, fifth and sixth expressions (from the top) are NOT polynomials, and the reason in each case is that the expression has one or more negative powers of x in it.
Kenya exchanges $200 for euros (€). Suppose the conversion rate is €1 = $1.321. How many euros should Kenya receive?
€264.20
€151.40
€132.10
€66.05
Answer:
The second option, or option b
Step-by-step explanation:
200/1.321 = 151.4
Answer: € 151.40
Step-by-step explanation:
€1 = $1.321
200/1.321 = €151.40
Rewrite using a negative exponent.
5/x ^2
When Grace runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 2 seconds. What percentage of races will her finishing time be faster than 79 seconds, to the nearest tenth?
Answer:
0.07
Step-by-step explanation:
Solve for x: x + 18 = -37 A. x = -55 B. x = -18 C. x = -19 D. x = 14
Answer:
A. x= -55
Step-by-step explanation:
got it
Bill receives a monthly stipend of $800. He also works at a bookstore making $8 an hour. He wants a monthly income of $1,200. How many hours does he need to work each month?
Answer:
150 hours
Step-by-step explanation:
Bill receives $800 as monthly stipend. But after this statement, it says Bill also works at a bookstore. So, it should mean that Bill does not receive $800 from the bookstore. He receives $800 from another job because of the word "also" which is mentioned in the second statement.
If the question is, to find out the number of hours Bill has to work each month if he assumes his monthly income to be $1,200 then 1200/8 = 150
But if the question is trying to mean that Bill receives $800 as a monthly stipend from the bookstore then this answer is wrong.
Then, we would have to calculate the difference.
$1200 - $800 = $420
Time = $420/8 = 50 hours.
Everything depends on the question. The question however needs some explanation, because this question is not written in a clear way.
Suppose that in circle with center P, and a central angle, ∠OPQ, intersects minor arc OQ, where the measure of arc OQ = 82◦, and the measure of ∠OPQ is (5x – 3) ◦. What is the value of x?
Answer:
Central Angle OPQ = Arc OQ = 82°
5x - 3 = 82°
5x = 85°
x = 17 degrees
Step-by-step explanation:
What was the mean number of peas in a pod 2 4 5 6 6 7 8 10 14 18
Answer:
The mean is 7.5
Step-by-step explanation:
1.add all of the numbers together
2.Divide by 10 since you have 10 numbers to add
Hope this Helps!
Use the distributive property to factor out y.
5y-3y + 12
The new expression becomes
O By+ 12
0-2y+ 12
0 2y+ 12
O 147
________________________________
5y-3y+12
=2y+12
So the new expression becomes 2y+12
hope it helps
Good luck on your assignment
________________________________
Answer:
2y+12
Step-by-step explanation:
Help quickly! Please find X
Answer:
About 4.5
Step-by-step explanation:
Since the full base has length 8, half of it must have length 4. Now, using the Pythagorean theorem, you can find x:
[tex]x=\sqrt{6^2-4^2}=\sqrt{36-16}=\sqrt{20}\approx 4.5[/tex] or answer choice D
Hope this helps!
Answer:the answer is 4
Step-by-step explanation:
Find the greatest and the smallest numbers that can be written using three ‘ones’, decimal points and/or exponents.
Answer:
Biggest = 111
Smallest = 0.1^(11) = 0.00000000001
Step-by-step explanation:
The smallest number I believe you can get is 0.1^11 this results in a number of 0.00000000001 and I believe the biggest number is 111.
Alex measured the rainfall on his property to be 10.5 cm in June which he calculated to be a 35% increase compared to the previous month. how much had it rained in may explain the steps you took to turn in the solution
Answer: 3.675 cm
Step-by-step explanation:
June was 35% more compared to May
35% of 10.5 cm = 3.675 cm in May
what is the measure of DAB
It's known as exterior angle theorem...The sum of angleB + angle C is equal to angle DAB....
That means 65+61 = 126...
Angle DAB =126
2 Points
What is the slope of the line that contains the points in the table?
y
23
-5
-2
14
1
5
3
A. 3
B. -100
D. -3
Answer:
D. -3
Step-by-step explanation:
The table is:
x | y
-5 | 23
-2 | 14
1 | 5
To find the slope, you need two points (x1, y1) and (x2, y2) and the next formula:
slope = (y2 - y1)/(x2 - x1)
Using (-2, 14) and (1, 5) (other combinations are also possible) the slope is:
slope = (5 - 14)/(1 - (-2)) = -3
The line segment AB with endpoints A (–3, 6) and B (9, 12) is dilated with a scale factor 2∕3 about the origin. Find the endpoints of the dilated line segment. answers: A) (4, –2), (6, 8) B) (–2, 4), (6, 8) C) (–2, 4), (8, 6) D) (2, 4), (6, 8)
Answer:
B. The endpoint of the dilated line is (-2,4),(6,8)
Step-by-step explanation:
Given
Line segment AB
Endpoints: A(-3,6) and B(9,12)
Scale Factor: 2/3 about the origin
Required
Find the end points of the dilated line
From the question, we understand that the line segment is dilated about the origin;
The keywords about the origin implies that, to get the endpoints of the dilated line, we simply multiply the coordinates of of the original line by the scale factor;
This is shown below;
[tex]For\ A = (-3,6);[/tex]
The new endpoints become
[tex]A' = \frac{2}{3} A[/tex]
[tex]A' = \frac{2}{3} (-3,6)[/tex]
[tex]A' = (\frac{2}{3} * -3, \frac{2}{3} * 6)[/tex]
[tex]A' = (\frac{2* -3}{3}, \frac{2 * 6}{3})[/tex]
[tex]A' = (\frac{-6}{3}, \frac{12}{3})[/tex]
[tex]A' = (-2, 4)[/tex]
[tex]For\ B = (9, 12);[/tex]
The new endpoints become
[tex]B' = \frac{2}{3} B[/tex]
[tex]B' = \frac{2}{3} (9, 12)[/tex]
[tex]B' = (\frac{2}{3} * 9, \frac{2}{3} * 12)[/tex]
[tex]B' = (\frac{2* 9}{3}, \frac{2 * 12}{3})[/tex]
[tex]B' = (\frac{18}{3}, \frac{24}{3})[/tex]
[tex]B' = (6, 8)[/tex]
Hence, the endpoint of the dilated line is (-2,4),(6,8)
Answer:
3/2
Step-by-step explanation:
