Answer:
x=2; the extraneous root x=42.
All the details are in the attached picture, the answer is marked with red colour.
The radical equation 2 + 2x - 3. √(x + 7) has a solution set z = 2 and an extraneous root = -7.
To solve the equation, we can start by simplifying the radical. We get:
2 + 2x - 3√(x + 7) = 0
We can then move the constant term to the other side of the equation. We get:
2x - 3√(x + 7) = -2
We can then multiply both sides of the equation by -1. We get:
3√(x + 7) - 2x = 2
We can then square both sides of the equation. We get:
9(x + 7) - 12x * √(x + 7) + 4x² = 4
We can then rearrange the terms on the left-hand side of the equation. We get:
4x² - 12x * √(x + 7) + 5 = 0
We can then factor the expression on the left-hand side of the equation. We get:
(2x - 1)(2x - 5) = 0
This gives us two solutions, x = 1/2 and x = 5.
The solution x = 1/2 is a valid solution because it does not make the radical expression undefined. However, the solution x = 5 is an extraneous root because it does make the radical expression undefined.
Therefore, the solution set z = 2 and the extraneous root = -7.
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If < W and < Y are supplementary, and < W = 121 °, then what would < Y measure?
Select one:
a. 121 °
b. 69 °
c. 59 °
d. 13 °
Answer:
Option c. 59°
Step-by-step explanation:
<W+<Y=180
121+<Y=180
<Y=180-121
<Y=59
Answered by GAUTHMATH
Which of the following are possible
side lengths for a triangle?
A. 4, 9,4
B. 3, 8, 12
C. 8,8,9
As we know,
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
A. 4, 9, 4
[tex]4 + 9 > 4[/tex]
[tex]9 + 4 > 4[/tex]
[tex]4 + 4 < 9[/tex]
B. 3, 8, 12
[tex]3 + 8 < 12[/tex]
[tex]8 + 12 > 3[/tex]
[tex]12 + 3 > 8[/tex]
C. 8, 8, 9
[tex]8 + 8 > 9[/tex]
[tex]8 + 9 > 8[/tex]
[tex]9 + 8 > 8[/tex]
By observing the above,
the possible side lengths of a triangle are C. 8, 8, 9.
[tex]\frac {n! + (n + 1)!} {n!}[/tex]
help me in this please
(n! + (n + 1)!) / n! = n!/n! + (n + 1)!/n! = 1 + (n + 1) = n + 2
because (n + 1)! = (n + 1)n!.
The nth term for the question
Answer:
Step-by-step explanation:
1) nth therm = dn + (a - d)
-10n + (11+10)
-10n + 21
t11 = -110 + 21 = -89
2) nth therm = 3n + (-66 - 3)
3n - 69
t16 = 48 - 69 = -21
What is the radius of the circle: x^2+y^2=4
1. -2
2. -4
3. 4
4. 2
Answer:
2
Step-by-step explanation:
→ The radius of a circle is square root the 4
2
Please help me!
The Farmer's Ranch House
9. The farmer's house is shown in the diagram below. He wants to build a screened-in patio on the back of his house.
Use the figure to answer the questions. (6 points)
a The area of the patio is planned to be (x + 10x - 200) square feet. What will the length be?
Patio
Patio
**10) - 0-10)
Original
House
b.
What is the area of the original house in simplest form?
Terigth
c
The farmer decides to extend the width of the patio. The area of the patio with the extension is now (x2 + 12x-160) square feet. By how
many feet will the patio be extended from what you found in part a?
Answer:
The answer is below
Step-by-step explanation:
a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:
[tex]Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20[/tex]
b) Area of original house = length of house * breadth of house
The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:
Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200
Area of original house = x² + 30x + 200
c) If the width is extended, hence:
[tex]Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet[/tex]
I need help asap!! round your answer to the Nearest tenth.
Answer:
25.1
Step-by-step explanation:
the volume of a cone is V=πr^2(h /3)
PLEASE HELP!!! Find the equation of the line passing through the point that (4,-1)that is parallel to the line 2x-3y=9
Answer:
y=2/3x-11/3
Step-by-step explanation:
line is parallel so the gradient will be the same ( m=2/3)
using the point (4,-1)
y=2/3x+c
-1=2/3*4+c
-1=8/3+c
c= -11/3
equation ---> y=2/3x-11/3
expand the following:
a) 8(×-2y)
Answer:
8x-16y
Step-by-step explanation:
8*x-8*2y
8x-16y
Answer.
8x - 16y
Explained in the picture atteached:
please write your answer with explanation
Answer:
Step-by-step explanation:
If cost price (CP) is greater than selling price (SP) , then the item is sold for loss.
Loss = CP - SP
Loss% = [tex]\frac{loss}{CP}*100[/tex]
If SP is greater than Cp, then the item is sold for a profit.
Profit =SP -CP
Gain % = [tex]\frac{gain}{CP}*100[/tex]
a) CP = $50 ; SP = $30 ; CP > SP, loss
Loss = 50 - 30 = $ 20
Loss % = [tex]\frac{20}{50}*100=20*2[/tex]
= 40% loss
b) CP = £ 5000 ; SP = £6250 ; SP > CP , Profit
Profit = 6250 - 5000 = £ 1250
Profit % = [tex]\frac{1250}{5000}*100=25[/tex]
25% Profit
Which of the following is an arithmetic sequence?
The perimeter of a rectangular plot is 36 metres. The length is 6 metres more than the width. What is the area of the rectangular plot?
Answer:
72 m^2
Step-by-step explanation:
Perimeter = 36
Length + width = 18
w + w + 6 = 18
2w + 6 = 18
2w = 12
w = 6
Length + 6 = 18
Length = 12
Area = 6 * 12 = 72 m^2
y = 2x + 3
y=2x-1
The system has how many solutions?
one solution
two solutions
no solution
an infinite number of solutions
Instructions: Problem 1 ! Find the missing angle in the image below. Do not include spaces in your answers
Answer:
40 degrees
Step-by-step explanation:
The 100 degree angle is supplementary to angle CED. This means CED will end up being 80 degrees. Since the angles in all triangles equate to 180 degrees 80 + 60 + angle D must equal 180 degrees. Therefore, angle D has to be 40 degrees.
Find the slope between the points (−3,−5) and (10,-5)
. Enter DNE if the slope between the points is undefined.
Answer:
0
Step-by-step explanation:
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] m = \dfrac{-5 - (-5)}{-3 - 10} [/tex]
[tex] m = \dfrac{0}{-13} [/tex]
[tex] m = 0 [/tex]
from -3 to 10 are 13 steps to the right and from -5 to -5 0 steps up or down.
devide the steps up by the steps to the right
0 / 13 = 0
in this case it's obvious, but I hope you see the method how to do this. you would normally get a more interesting fraction as a slope.
PLSSS help me solve this question
Answer:
(3,-5)
Step-by-step explanation:
The line y=-x is a positively sloped line that when reflected across changes all signs to their opposite counterpart. Positivee to negative, negative to positive.
Find the value please!!!
the answer is in the picture
For what value of k will (k – 5)x²+ 2ky²-5x + 6y – 3 = 0 represents a circle? (
Answer:
This isn't going to be a circle even if we choose k to be -5.
I think there has to be an error in the question.
Step-by-step explanation:
We want the coefficient of x^2 and y^2 to be the same so we will want to solve:
k-5=2k
Subtract k on both sides:
-5=k
You should verify it will give a circle.
(k – 5)x²+ 2ky²-5x + 6y – 3 = 0 with k=-5:
(-5– 5)x²+ 2*-5y²-5x + 6y – 3 = 0
-10x²+ -10y²-5x + 6y – 3 = 0
Add 3 on both sides:
-10x²+ -10y²-5x + 6y = 3
Divide both sides by -10:
x²+ y²+5/10x -6/10y = -3/10
Gather the x's together and gather the y's together:
x²+5/10x+y²-6/10y = -3/10
We will begin to take steps to complete square for each the x part and the y part.
For each v^2+kv, add (k/2)^2 with goal to write as (x+k/2)^2. Remember whatever you do to one side you must do to the other.
x²+5/10x+(5/[2×10])^2+y²-6/10y+(-6/[2×10])^2 = -3/10+(5/[2×10])^2+(-6/[2×10])^2
Since radius square is not positive we can stop here. The radius has to be a real number after all. If you aren't convinced you can continue to write in center-radius form.
(x+1/4)²+(y-3/10)² = -3/10+1/16+9/100
(x+1/4)²+(y-3/10)² = -3/10+1/16+9/100
(x+1/4)²+(y-3/10)² = -59/400
Which of the following best describes the line of symmetry?
A. The line that is perpendicular to the design
B. The line that is parallel to the design
C. The line that divides the design into two similar parts
D. The line that divides the design into two congruent parts
Answer:
C the line that divides the design into two similar parts
The line of symmetry divides the design into two similar parts.
What is a line of symmetry?"The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves. "
A line divides a design into two parts.
If the line is described as the line of symmetry, then the two parts that are divided by this line are similar parts.
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1. What is the perimeter of the figure below. Simplify.
4x^3-5x 2x^3+6x 6x^3+x
Answer:
[tex]12x^3+2x[/tex]
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of its sides.
The sides in the triangle shown have lengths [tex]2x^3+6x[/tex], [tex]4x^3-5x[/tex], and [tex]6x^3+x[/tex] in no specific order.
Since its perimeter is given by the sum of its sides, the perimeter is equal to:
[tex]2x^3+6x+4x^3-5x+6x^3+x[/tex]
Combine like terms:
[tex]\boxed{12x^3+2x}[/tex]
In a group of 26 pupils, 3 play the flute only.
5 play the piano only.
7 play neither instrument.
How many pupils play both instruments?
Here is a Venn diagram:
PLEASE HELPP ILL GIVE 20 POINTS
Answer:
C=20
Step-by-step explanation:
Is -3y = 5x + 4 perpendicular
Answer:
no it is not perpedicular
Step-by-step explanation:
I plugged the equation into a graphing calculator and the line does not appear to be perpendicular
Answer:
3y = 5x+4
3y=9x
yx=9/3
yx=3
Show how you arrived at your answers.
Kenzie says that x? + 25 can be factored into (x + 5). Ariana says that
it cannot. Who is correct? Explain your answer.
Step-by-step explanation:
if that's x^2+25
they can be factored to x+5
because the factor of x^2 is x cause x multiplied by x is x^2 and the factor of 25 is 5 cause 5×5 is 25
Type the correct answer in each box.
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was
2
times the weight of the first fish, another was
2
more than
3
times the weight of the first fish, the next was
1
2
the weight of the first fish, and the last was
3
5
the weight of the first fish.
Bridget’s dad caught four fish. The first fish he caught weighed
2
more than
3
times the weight of the first fish caught that day.
One fish weighed
4
5
the weight of the first fish caught that day, one weighed
4
more than
2
times the weight of the first fish caught that day, and the last weighed
1
2
the weight of the first fish caught that day.
Answer:
PLZZ MARK ME BRAINLIEST..!
Step-by-step explanation:
Bridgets fish: f , 2f, 3f+2 , 1/2f, 3/5f
Add for total weight: 7 1/10 f +2
Dads fish: 3f+2, 4/5f, 2f+4, 1/2f
Add for total weight: 6 3/10f +6
set the 2 total weights equal:
6 3/10f +6 = 7 1/10f +2
Subtract 6 3/10f from each side:
6 = 8/10f + 2
Subtract 2 from each side:
4 = 8/10f
Divide both sides by 8/10:
f = 5
Bridget's first fish weighed 5 ounces.
Dads first fish weighed: 2 more than 3 times :3(5) + 2 = 15 +2 = 17 ounces.
If a set of scores for a variable is displayed in a frequency distribution polygon, which scale of measurement was used to measure the variable
Given: The set of scores for a variable is displayed in a frequency distribution polygon.
To find: We need to find which scale of measurement was used to measure the variable
Solution: A frequency distribution table is always either in interval or in ration scale.
Work out the area of the shaded
Hi there!
[tex]\large\boxed{73m^2}}[/tex]
Once again, divide the figure into 3 rectangles:
Top rectangle:
3m × 5m = 15m²
Long rectangle (subtract 5m from 9m to get the width):
12m × 4m = 48m²
Bottom rectangle:
2m × 5m = 10m²
Add up areas:
15m² + 48m² + 10m² = 73m²
Find the distance between (1, 2) and (5,2)
The points lie in______
The distance is________
the 3 three questions
Answer:
Step-by-step explanation:
#2 Should be many to one; the reason for this is when doing functions a proper one will have one input to one output.
#3 Should be D; same reasoning as above.
And sorry I am at a loss for #1.
Someone help me?????
Answer:
A. y = | x - 6 | - 3
Step-by-step explanation:
Hope this is helpful
Answer:
D
Step-by-step explanation:
when you look at the graph you can notice a kind of a curve at that point x is -6 and Y is -3 so what u have to do is replace -6 in position of x in the 4 answers and the one who's Y = -3 is your answer