Step-by-step explanation:
that kind of wording is always misleading.
please give my regards and comments to your teacher.
a square root has ALWAYS 2 solutions : a positive AND a negative one.
in that sense the negative solution to a square root is NOT an extraneous solution.
only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.
so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.
so,
x + 4 = sqrt(x + 10)
since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.
x = -1
-1 + 4 = sqrt(-1 + 10)
3 = sqrt(9) = 3 (actually, it is ±3)
so, x = -1 is a real solution.
x = -6
-6 + 4 = sqrt(-6 + 10)
-2 = sqrt(4) = 2 (actually, it is ±2)
so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),
x = -6 is an extraneous solution.
therefore, the third answer (c) is the "correct" answer.
but actually, formally, the second answer (b) is the truly correct answer.
( 100 points + brain ) My dropshipping business makes me 11,000$ - 40,000$ a month, At this rate how much money could I make in a year? how much money could I make in 20 years? how much money could I make in 60 years?
Answer:
One year: Between $132,000 and $480,000.
20 years: Between $2,640,000 and $9,600,000.
60 years: Between $7,920,000 and $28,800,000.
Step-by-step explanation:
If it makes between 11,000 and 40,000 a month, you should take both values and average them or make an estimate. Since there are 12 months in a year, 11,000*12 = $132,000 minimum, 40,000*12 = $480,000 maximum.
In 20 years, 132,000*20= $2,640,000 minimum, 480,000*20 = $9,600,000 maximum.
In 60 years, 2,640,000*3 = $7,920,000 minimum, 9,600,000*3 = $28,800,000 maximum.
If you want to be more specific, you need to find the average number of times you make certain amounts of money per month to find how likely it is to make a certain amount.
Answer:
taking my points back
Step-by-step explanation:
Solve for x: 12x= 36
Please show all the steps that were given above that you must take to solve for x.
Step-by-step explanation:
x=36/12
x=2
I hope it's helpful for you12x = 36
x = 36÷12
x = 3
Hope it helps......
which prism has the greatest value
Please help me do this mathematics question genius
The changes in Z would be = 6.1× 10^-4.
Calculation of the unknown valueZ = Sin (x³ +y³)
Where X = 0.3
y = 0.2
Z= Sin ( 0.3³ + 0.2³)
Z= Sin ( 0.027 + 0.008)
Z= Sin ( 0.035)
Z= 6.1× 10^-4
Therefore, the changes in Z would be = 6.1× 10^-4.
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What is the slope of the line passing through the points (2, 5) and (0, -4)?
Show all your work.
Leave your answer as a fraction
Answer:
slope = 9/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-4 - 5/0- 2 = 9/2
A square has a perimeter of 40 feet. Find the length of the
diagonal of the square.
Answer:
14.14
Step-by-step explanation:
Answer:
The length of the diagonal of the square is about 14.142 feet
Step-by-step explanation:
Step 1: Determine the length
[tex]P = 4(l)[/tex]
[tex]40\ ft = 4(l)[/tex]
[tex]\frac{40\ ft}{4}=\frac{4(l)}{4}[/tex]
[tex]10\ ft = l[/tex]
Step 2: Determine the diagonal length
Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]
a and b are going to be the sides of the square which are both 10 ft so we just plug those in and solve for c
[tex](10)^2 +(10)^2 =c^2[/tex]
[tex]100+100=c^2[/tex]
[tex]\sqrt{200}=\sqrt{c^2}[/tex]
[tex]14.142=c[/tex]
Answer: The length of the diagonal of the square is about 14.142 feet
A midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 120. 132. 160.
The midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 132.
How to calculate the midpoint?The value of f(1/2) will be:
= 2(1/2)(1/2 - 4)(1/2 - 8)
= 105/4
The value of f(3/2) will be:
= 2(3/2)(3/2 - 4)(3/2 - 8)
= 195/4
The value of f(5/2) will be:
= 2(5/2)(5/2 - 4)(5/2 - 8)
= 165/4
The value of f(7/2) will be:
= 2(7/2)(7/2 - 4(7/2 - 8)
= 63/4
Therefore, the midpoint approximation will be:
= 1/4(105 + 195 + 165 + 63)
= 132
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Harry invests $1000 in an investment account that earns 6% interest, compounded annually. How much money will he have in the account after 30 years?
the answer to that question is 1800
Convert 85° to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
answer :
[tex]C=\frac{265}{9}[/tex]
work:
[tex]F=85[/tex] °[tex]C[/tex]
[tex]F= 85[/tex] into [tex]C=\frac{5}{9}(F-32)[/tex]
[tex]C=\frac{5}{9}[/tex] x [tex](85-32)[/tex]
[tex]C=\frac{265}{9}[/tex]
4x+3y=6
-4x+2y=14
Solve the system of equations.
A. x= 1/2, y=3
B. x=3, y =1/2
C. x=4, y = -3/2
D. x=-3/2, y = 4
Answer:
D
Step-by-step explanation:
4x + 3y = 6
-4x + 2y = 14
0 + 5y / 5 = 20/ 5 = 4 = y
4x + 3(4) = 6
4x + 12 - 12 = 6 - 12
4x / 4 = -6 / 4 = -3 / 2 =x
PLEASE HELP!!!!!!!!
Note: please add the answer next to the number its from so I can know which question was answered
What is the value of x in | - 6| = x? O 6 and -6 00 06 -6 HOURME
Answer:
I believe, 6.
Step-by-step explanation:
Not sure if the rest of the question is the answer choices but the absolute of any number, is it's exact opposite. The reason for this is that an absolute number, or |?| is equal to whatever distance it is from 0. Since adding 1, and subtracting 1, both do such but in opposite directions, the absolute value of both would be 1.
find tan0 please help fast!
Answer:
Tan(51.06) = 1.24 so the correct answer is A
Step-by-step explanation:
Sin0 = 7/9
0 =Arcsin(7/9)
0 =51.06
So,
Tan(51.06) = 1.24 so the correct answer is A
Answer:
A. [tex]\frac{7\sqrt{2} }{8}[/tex]
Step-by-step explanation:
Finding the missing side :
7² + x² = 9²
x² + 49 = 81
x² = 32
x = 4√2
Taking the tan value :
tanθ = 7/(4√2)
tanθ = 7(4√2)/4√2(4√2)
tanθ = 28√2/32
tanθ = [tex]\frac{7\sqrt{2} }{8}[/tex]
En el sistema, encontrar el doble de y:
2x + y = 5
x + y = 4
a) 6
b) 4
c) 3
d) 2
Answer:
y=3
x=1
Step-by-step explanation:
1 by substitution method
2x+y=5 (1)
x+y=4 (2)
find x in eq 2
x=4-y
put the value in eq 1
2x+y=5
2(4-y)+y=5
8-2y+y=5
8-y=5
-y=5-8
-y=-3
y = 3
x=4-y
x=4-3
x=3
hope it helps you
please mark it as brainliest
hi can anyone solve my math problem
Answer:
The solutions to this equation are x = -8/9 and x = -16/3.
Step-by-step explanation:
We have this equation here:
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+\frac{6}{3} |[/tex]First, let's simplify the right sight of the equation by simplifying 6/3 to 2.
[tex]\displaystyle \frac{1}{3}|x-4|=\frac{2}{3} x+2|x+2 |[/tex]Multiply both sides of the equation by 3 in order to get rid of the fractions.
[tex]|x-4|=2x+6|x+2|[/tex]Move the terms on either side of the equation to set them equal to 0.
[tex]|x-4|-2x-6|x+2|=0[/tex]Now, we can split this equation up into 4 possible cases. In each case, we make the absolute values negative or positive.
Case #1 (first absolute value: positive; second absolute value: positive)[tex](x-4)-2x-6(x+2)=0[/tex]Simplify this equation by distributing -6 inside the parentheses.
[tex]x-4-2x-6x-12=0[/tex]Combine like terms.
[tex]-7x-16=0[/tex]Add 16 to both sides of the equation and divide by -7.
[tex]\displaystyle \boxed{x=-\frac{16}{7}}[/tex]Case #2 (first absolute value: negative; second absolute value: positive)[tex]-(x-4)-2x-6(x+2)=0[/tex]Distribute the negative sign and -6 inside of their respective parentheses.
[tex]-x+4-2x-6x-12=0[/tex]Combine like terms.
[tex]-9x-8=0[/tex]Add 8 to both sides of the equation and divide by -9.
[tex]\displaystyle \boxed{x=-\frac{8}{9}}[/tex]Case #3 (first absolute value: positive; second absolute value: negative)[tex](x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative sign inside the parentheses first.
[tex]x-4-2x-6(-x-2)=0[/tex]Now, distribute -6 inside the parentheses.
[tex]x-4-2x+6x+12=0[/tex]Combine like terms.
[tex]5x+8=0[/tex]Subtract 8 from both sides of the equation and divide by 5.
[tex]\displaystyle \boxed{ x=-\frac{8}{5}}[/tex]Case #4 (first absolute value: negative; second absolute value: negative)[tex]-(x-4)-2x-6[-(x+2)]=0[/tex]Distribute the negative signs inside the parentheses first.
[tex]-x+4-2x-6(-x-2)=0[/tex]Distribute -6 inside the parentheses.
[tex]-x+4-2x+6x+12=0[/tex]Combine like terms.
[tex]3x+16=0[/tex]Subtract 16 from both sides of the equation and divide by 3.
[tex]\displaystyle \boxed{x=-\frac{16}{3}}[/tex]Extraneous SolutionsWhenever we solve problems with absolute values, we will always need to check for extraneous solutions.
Definition: These are solutions that may come up while solving but do not actually fit in the domain of the original problem.
Checking for these is tedious, but it will help eliminate wrong answers, so let's plug every "solution" for x that we found back into the original equation.
1) x = -16/7Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{7}) -4|=\frac{2}{3} (-\frac{16}{7}) +2|(-\frac{16}{7}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{21} =-\frac{20}{21}[/tex]Since this equation is NOT true, this means that x = -16/7 is NOT A SOLUTION.
2) x = -8/9Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{9}) -4|=\frac{2}{3} (-\frac{8}{9}) +2|(-\frac{8}{9}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{44}{27} =\frac{44}{27}[/tex]Since this equation IS true, this means that x = -8/9 IS A SOLUTION.
3) x = -8/5Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{8}{5}) -4|=\frac{2}{3} (-\frac{8}{5}) +2|(-\frac{8}{5}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{15} =-\frac{4}{15}[/tex]Since this equation is NOT true, this means that x = -8/5 is NOT A SOLUTION.
4) x = -16/3Substitute this value back into the original equation.
[tex]\displaystyle \frac{1}{3}|(-\frac{16}{3}) -4|=\frac{2}{3} (-\frac{16}{3}) +2|(-\frac{16}{3}) +\frac{6}{3} |[/tex]If we do all the calculations correctly, we will get:
[tex]\displaystyle \frac{28}{9} =\frac{28}{9}[/tex]Since this equation IS true, this means that x = -16/3 IS A SOLUTION.
Final AnswerThe two true solutions of the double absolute value equation, shown above, are:
[tex]\displaystyle \boxed{-\frac{8}{9} } \ \ \& \ \ \boxed{-\frac{16}{3}}[/tex]Answer:
x = -16/3 or -8/9
Step-by-step explanation:
The equation can be rewritten as a piecewise linear function with two breakpoints, or three domain regions. Each breakpoint is at the value of x where the argument of the absolute value function is zero: at x=4 and x=-2.
For each absolute value, we have ...
|q| = -q for q < 0
|q| = q for q ≥ 0
Then the three parts of the domain are ...
x < -2 . . . . . . . . where |x +2| has its vertex-2 ≤ x < 4 . . . . . between the vertices4 ≤ x . . . . . . . . . where |x -4| has its vertex__
Subtracting the right side, the equation becomes ...
1/3|x -4| -2/3x -2|x +2| = 0
Then the three piecewise functions are ...
x < -2Both absolute value arguments are negated.
1/3(-(x -4)) -2/3x -2(-(x +2)) = 0
x(-1/3 -2/3 +2) +4/3 +4 = 0 . . . . . collect terms
x +5 1/3 = 0 . . . . . . . simplify
x = -5 1/3 . . . . . . . . . subtract 5 1/3. This result is in the domain
__
-2 ≤ x < 4Only the argument of |x -4| is negated.
1/3(-(x -4)) -2/3x -2(x +2) = 0
x(-1/3 -2/3 -2) +4/3 -4 = 0 . . . . collect terms
-3x -8/3 = 0 . . . . . . . simplify
-3x = 8/3 . . . . . . . add 8/3
x = -8/9 . . . . . divide by -3. This result is in the domain
__
4 ≤ xNeither absolute value function argument is negated.
1/3(x -4) -2/3x -2(x +2) = 0
x(1/3 -2/3 -2) -4/3 -4 = 0 . . . . . collect terms
-7/3x -8/3 = 0 . . . . . . . . . simplify
-7/3x = 8/3 . . . . . . . . add 8/3
x = -8/7 . . . . . . . . . divide by -7/3. This result is not in the domain.
There is no solution in this region.
__
The solutions are ...
x = -5 1/3x = -8/9Which of the following are always congruent?
Answer:
B. Vertical angles
Step-by-step explanation:
i want to know this factorization
. Estimate the sum of 277 and 854 and write them in Roman numerals.
Answer:
The answer is MC = 1100. The real answer is 1131 but I have estimated the answer to the nearest hundred.
Step-by-step explanation:
I just added them up to get the real answer. The real answer is 1131 but I have estimated the answer to the nearest hundred.
triunghiul echilateral DEF este inscris in cercul C(O, 4radical6). Calculati aria triunghiului DEF.
Answer:
[tex]\green{ \rule{500pt}{999999pt}}[/tex]
Jeff sells shirts at a store in the mall. Which group should he survey to determine which color of shirt will have the greatest number sold?
Female customers
customers who are wearing blue
200 random customers
10 friends at work
The 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
Jeff sells shirts at a store in the mall.
The selecting the colour of the shirts is subjective.
It also depends on that how many colours that store sell.
Female customers cannot be an option because men also buy shirts and affect the result of the survey.
Customers who are wearing blue data only tells that how many blue shirts sold.
200 random customers. 200 is a sample from a population, so it will give appropriate results about the colour of shirt will have the greatest number sold
Thus, the 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.
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If our statement was < β is congruent to < α, the reason would be _____.
Answer:
Step-by-step explanation:
Vertical angles theorem.
It the UK they are called opposite angles,
How many three digit numbers can you make by arranging the numbers 5, 4, and 9.
okay,here is about a formula.
n=2x
where x is the numbers.
n=2×3
n=6.
therefore the three digit numbers which can be obtained is 6.
Suppose that you have $14,000 to invest and you are trying to decide between investing in project A or project B. If you invest in
project A, you will receive a payment of $17,000 at the end of 3 years. If you invest in project B, you will receive a payment of $56,000
at the end of 23 years. The annual interest rate is 6 percent and both projects carry no risk.
Instructions: Round your answers to the nearest dollar. Do not round your intermediate calculations.
a. What is the present value of each project? Enter your answers in the table below.
Present Value
Project A =
$
Project B =
$
b. Which project will you choose for your investment?
Project A
Project B
Use the equation below to find A, if 1 = 6 and w = 3.
A = lw
Answer:
l=6, w=3
And A is the multiplication of l and w
A=6×3
What is the area of this figure? Please help
Answer:
369.5 ft²
Step-by-step explanation:
Area of figure :
Area (rectangle 1) + Area (rectangle 2) + Area (triangle 1) + Area (triangle 2)
5 x 4 + 13 x 8 + 1/2 x 23 x 13 + 1/2 x 24 x 820 + 104 + 149.5 + 96124 + 96 + 149.5220 + 149.5369.5 ft²Answer:
369.5 ft²
Step-by-step explanation:
Separate the figure into 2 rectangles and 2 triangles.
(see attached image)
Area 1
Area of a rectangle = width × length
= 4 × 5
= 20 ft²
Area 2
Area of a rectangle = width × length
= 8 × (4 + 4 + 5)
= 8 × 13
= 104 ft²
Area 3
Area of a triangle = 1/2 × base × height
= 1/2 × (6 + 4 + 5 + 4 - 6) × 23
= 1/2 × 13 × 23
= 149.5 ft²
Area 4
Area of a triangle = 1/2 × base × height
= 1/2 × 8 × (21 + 8 - 5)
= 1/2 × 8 × 24
= 96 ft²
Total Area
Area 1 + Area 2 + Area 3 + Area 2 = 20 + 104 + 149.5 + 96
= 369.5 ft²
Please help me ojn this question
Answer:
T4 = 162 T5 = 486 T6 = 1458
Explanation:
the pattern is multiply the previous number by 3
so 6 x 3 = 18
18 x 3 = 54
54 x 3 = 162 and so on.
Which graph represents the function f(x) = –x2 + 5? On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4). On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9). On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9). On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).
Answer:
The graph in the attached figure
Step-by-step explanation:
we have the quadratic function
[tex]f(x)=-x^2+5[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Remember that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem
a=-1
(h,k)=(0,5) ----> vertex
The y-intercept is the point (0,5) ---> value of y when the value of x is equal to zero (is the same point that the vertex)
The x-intercepts are the points --->values of x when the value of y is equal to zero
using a graphing tool
The graph in the attached figure
Answer:
A on edge
Step-by-step explanation:
i took the test
please solve the given problem
Answer:
x = -47.1
x = -3.35454... (2-digit repeat)
Step-by-step explanation:
Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.
These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...
x < -7-7 ≤ x < -5/2In those regions, the equation simplifies to ...
x < -72(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))
x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms
15.7 = -1/3x . . . . . . add 5/2
x = -47.1 . . . . . . . multiply by -3
__
-7 ≤ x < -5/22(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))
x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms
(-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8
x = -36.9/11 = -369/110
x = -3 39/110 ≈ -3.35454... (2-digit repeat)
Please please I need help. What is the value of X
Answer:
x = 25
Step-by-step explanation:
Solving
∠CAD = 1/2 ∡ CD180° - 90° - (2x)° = 1/2 (80°)2x = 90° - 40° = 50°x = 25
Help please bed asap thank you!!!
Answer:
hr
Step-by-step explanation:
