Answers
Answer:
\(x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}\)
(real solution) (imaginary solution)
Step-by-step explanation:
Substitution:For these type of questions, where the exponent is even, it helps to try to rewrite the equation into a quadratic equation as we have a closed formula (quadratic formula) to solve for the zeroes, and it's also just easier to deal with in general.
Let's say that: \(u=x^2\), now if we square both sides, \(u^2=x^4\), so from here we can substitute in u squared as x to the power of four.
This results in our following equation: \(49u^2-4\), from here we could use the quadratic formula, but you may notice a pattern here. We have a difference of squares: \(a^2-b^2=(a-b)(a+b)\)
\(49u^2\) can be written as \((7u)^2\) and \(4\) can be written as \(2^2\), this gives us our equation: \((7u)^2-2^2\implies (7u-2)(7u+2)\). If we use this definition of the equation on the left side, it gives us: \((7u-2)(7u+2)=0\) and this is very convenient as we can solve both of them individually.
Zero Property of Multiplication:Whenever we multiply any number (assuming it's defined) by zero, we should get.... zero. This intuitively makes sense as no matter how many times we add zero up (multiplication is repeated addition), we're always just going to have zero.
So when we have the equation: \(a*b=0\), if "a" is zero then regardless of what "b" is (assuming it's defined), then the product will be zero. If "b" is zero then regardless of what "a" is (assuming it's defined), then the product will be zero.
Now if we look back at our equation: \((7u-2)(7u+2)=0\), if \(7u-2=0\), then regardless of what \(7u+2\) is equal to, the product will be zero. Likewise, if \(7u+2=0\) then regardless of what \(7u-2\) is equal to, the product will be zero, thus making the equation true.
So to find the solutions to this, we find what makes \(7u-2=0 \text{ and }7u+2=0\) true. If we work them both out individually we
get:
\(7u-2=0\\7u=2\\u=\frac{2}{7}\\\\7u+2=0\\7u=-2\\u=-\frac{2}{7}\)
So now we have our two solutions right? Well remember we started off with a "x" variable, and the "u" is merely a substitution. If you recall, the "u" value is set equal to "x^2", so we can just plug that back in, so we can find the solutions in terms of x.
\(x^2=\frac{2}{7} \text{ and } x^2=-\frac{2}{7}\)
If we take the square root of both sides, we get:
\(x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm\sqrt{-\frac{2}{7}}\)
you'll notice in one of them, we're taking the square root of a negative number. This will result in imaginary solutions, if we factor out a "-1" and take the square root of that, we'll just get an "i" infront, giving us the solutions of: \(x=\pm\sqrt{\frac{2}{7}} \text{ and }x=\pm i\sqrt{\frac{2}{7}}\).
Related Questions
Solve.
9^(3x+1) = 27^2x
Answers
Answer: the equations has no solution
Step-by-step explanation:
\(9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution\)
Amanda bought 5 candles for $6 each, 4 lotions for $5 each, and 10 face masks for 3$ each. Write an expression to find the total amount Amanda spent.
please help it is due in 10 min
Answers
Answer:
$77 spent in all
Step-by-step explanation:
Find the equation of a line containing the following points. Write the equation in slope-intercept form.
(-2, 2) and (1, 2)
Preview
y =
Answers
Answer:
y=1/4x + 1.75
Step-by-step explanation:
1-2/2--2 = 1/4
2=1/4+b
b=1.75
-0.9 -1.2 which one is greatest
Answers
Answer:
-0.9
Step-by-step explanation:
it is closer to 0
Question 1
Solve the equation:
2z - 1 = -15
x=
Blank 1:
Answers
Answer:
z = - 7Step-by-step explanation:
\(2z - 1 = - 15\)
Move -1 to the right side of the equation
\(2z = - 15 + 1 \\ 2z = - 14\)
Divide both sides by 2
\( \frac{2z}{2} = - \frac{14}{2} \\ \)
We have the final answer as
z = - 7Hope this helps you
HELPPPP I WILL GIVE POINTS AND BRAINLIEST
Answers
Answer:
11 mm, 21 mm, and 16 mm.
Step-by-step explanation:
since 11+21>16, 11+ 16>21>11, You can form a triangle with 11,21,16
Solve for t 16-2t=3/2t+9
Answers
The value of t after solving is 2.
The expression is solved as :
Simplify 3/2t to 3t/2
16 - 2t = 3t/2 + 9
Multiply both sides by 2
32 - 4t = 3t + 18
Add 4t to both sideds
32 = 3t + 18 + 4t
Simplify 3t + 18 + 4t to 7t + 18
32 = 7t + 18
Subtract 18 from both sides
32 - 18 = 7t
Simplify 32 - 18 to 14
14 = 7t
Divide both sides by 7
14/7 = t
Simplify 14/7 to 2
2 = t
Switch sides
t = 2
Hence , the value of t after solving is 2.
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the point inside a circle that is the same distance from all the points on the circle
Answers
Answer:
the center
Step-by-step explanation:
The only point in the circle that is equidistant from the border is the center, and the lines that connect the center to the points on the circle is called the radius. All radii in a circle are congruent.
https://www.savvasrealize.com/community/proxy/assessment/61412825b25d49129d9db14d2c5aad64/images/e6f2866e-e41b-483b-8ca9-9b194d3eedd6
What is the area of the quadrilateral?
Answers
Answer:
I think the answer is 8 m. Hope this helps.
solve x and y for 5x−y=44−3=−3x−y=−12
Answers
The values of the variables are;
x = 7
y = -9
How to solve for the variablesFrom the information given, we have that;
5x−y=44
−3x−y=−12
Using the elimination method of solving simultaneous equations
Subtract equation (2) from equation (1), we get;
5x - y - (-3x - y) = 44 - (-12)
Now, expand the bracket
5x - y+ 3x + y = 56
collect the like terms
5x + 3x = 56
add the terms
8x = 56
Make 'x' the subject of formula
x= 7
Now, substitute the value of x in equation (2)
-3x - y = -12
-3(7) - y = -12
expand the bracket
-21 - y= - 12
collect like terms
-y = 9
y = -9
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What is the domain of the equation?
Answers
The domain of the equation include the following: D. all real numbers.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [-4, ∞}
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what is 73 division 84,649
Answers
73 division 84, 649 would give 8. 64 × 10^-4
How to determine the valueIn order to determine the value of the division, we have
= \(\frac{73}{84649}\)
Using the calculator, put the values in
We would have
= 8. 64 × 10^-4
Thus, 73 division 84, 649 would give 8. 64 × 10^-4
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Suppose a random sample of 30 one-bedroom rental listings in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the approximate probability that the sample mean rent price will be greater than $900?.
Answers
The approximate probability that the sample mean rent price will be greater than $900 is 0.003%.
In our scenario, we have a sample size of 30, which satisfies the condition for the CLT. Therefore, we can assume that the distribution of the sample mean rent price is approximately normal, with a mean of $880 (the population mean) and a standard deviation of $50/√(30).
Using the z-score formula, we can calculate the probability that the sample mean rent price will be greater than $900:
z = (x - μ) / (σ / √(n))
where x is the sample mean rent price we are interested in, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values we have:
z = (900 - 880) / (50 / √(30))
z = 4.02
We can use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 4.02. This probability is extremely small, approximately 0.00003 or 0.003%.
Therefore, we can say that the approximate probability that the sample mean rent price will be greater than $900 is very low, approximately 0.003%.
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Suppose that you are attempting to buy a house, and you are bargaining with the current owner over the sale price. The house is of value $200,000 to you and $100,000 to the current owner; so, if the price is between $100,000 and $200,000, then you would both be better off with the sale. Assume that bargaining takes place with alternating offers and that each stage of bargaining (an offer and a response) takes a full day to complete. If agreement is not reached after seven days of bargaining, then the opportunity for the sale disappears (you will have no house and the current owner has to keep the house forever). Suppose that you discount the future according to the discount factor 0.3 per day and the current owner discount the future at discount factor of 0.6 per day. The real estate agent has allowed you to decide whether you will make the first offer. Should you make the first offer or let the current owner make the first offer? Why? Suppose that you have to make the first offer, what will be your offer that is going to be acceptable to the current owner?
Answers
Answer:
the answer is to make the first offer!
Step-by-step explanation:
Since the surplus ($100000) is rapidly depleting, and though the second individual collects the whole surplus, it is already less than half of the surplus from the previous day. So, once you make the first bid, any offer above 100,000 would be fair to the second person and if he rejects the offer, he will only be able to get 100,000 the next day. You will raise the payout by 100000(1 ) this way.
Solve for k.19 - k = 4
Answers
Answer:
k=15
Explanation:
Given the equation:
\(19-k=4\)Step 1: Add k to both sides of the equation.
\(\begin{gathered} 19-k+k=k+4 \\ 19=k+4 \end{gathered}\)Step 2: Subtract 4 from both sides.
\(\begin{gathered} 19-4=k+4-4 \\ 15=k \end{gathered}\)The value of k is 15.
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
Answers
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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Squares are Rhombus but not rectangles true or false
Answers
Answer:
True
Step-by-step explanation:
Rhombus is a sideways SQUARE
Answer: True
if you turn a square 45 degrees to the side it is a rhombus
Suppose a loaded die has the following probability model: If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1
Answers
Answer:
the probability is 0.6
Step-by-step explanation:
The computation is shown below:
Let us assume the X would be the number appear on the top face
Now
= P(X = 1) ÷ P(X = 0)
= 0.3 ÷ 0.3 + 0.1 + 0.1
= 0.3 ÷ 0.5
= 0.6
hence, the probability is 0.6
4x-3(x+4)=7 i need to know this i need help with this.
Answers
Answer:
x=19
Step-by-step explanation:
4x-3x-12=7
x-12=7
x=7+12
x=19
Answer:
x=19
Step-by-step explanation:
first you would distribute the -3 to the x and the 4 which would give you
4x-3x-12=7
next you would combine like terms (there's always an invisible 1 one front of a variable)
x-12=7
then to get the variable by itself you would add 12 on each side
x=19
hope this helped :)
On thurday, lisa had 5$ in her bank account. she went to target to purchase stickers for her class. each pack of stickers cost 2$
write an inequality that represents s, the number of stickers purchased that resulted in her account ending in -10.
Answers
s = number of sticker packs purchased
x = ending balance in Lisa's bank account
We know that Lisa started with $5 and each pack of stickers costs $2. Therefore, her bank account balance after purchasing s packs of stickers is:
x = 5 - 2s
We also know that her account ended with a balance of -$10. Therefore, we can set up the following inequality:
x = 5 - 2s ≤ -10
Simplifying this inequality:
5 - 2s ≤ -10
-2s ≤ -15
s ≥ 7.5
However, since s represents the number of sticker packs, it must be a whole number. Therefore, the final inequality is:
s ≥ 8
This means that Lisa must have purchased at least 8 packs of stickers in order for her account to end with a balance of -$10.
Figure ABCD is a parallelogram. Is it also a rhombus? Why or why not?
D
5m
B
5 m
C
OA. It cannot be determined, because a parallelogram with congruent
adjacent sides may or may not be a rhombus.
B. No, because all four sides are congruent.
C. Yes, because adjacent sides are congruent.
D. No, because adjacent sides are congruent.
Answers
The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.
How to determine the true statement about the parallelogramGiven that
Figure ABCD is a parallelogram
Such that
Side lengths = 5 cm
This means that
The figure is a square
As a general rule
All squares can be classified as rhombus
This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length
Hence, the true statement is (c)
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Please answer this correctly
Answers
Answer:
The top plot represents the numbers above.
The smallest number is 50 so the line has to go to 50 and the biggest number is 100 so the line has to go to 100. Only the top graph goes all the way to 50.
Hope this helps
Step-by-step explanation:
Answer:
option 1
Step-by-step explanation:
Minimum number of swimmers = 50 &
Maximum number of swimmers = 100
Question 3 A 44-metres long fire-fighting ladder is leaned against a building, as shown in the diagram. The base of the ladder is 7 metres from the building and 3 metres above the ground. How high on the building will the ladder reach?
Answers
The ladder will reach a Height of approximately 43.46 meters on the building.
To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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 ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.
Using the Pythagorean theorem, we can set up the equation:
(Height of the building)^2 + 7^2 = 44^2
Simplifying the equation, we have:
(Height of the building)^2 + 49 = 1936
Subtracting 49 from both sides, we get:
(Height of the building)^2 = 1887
To find the height of the building, we take the square root of both sides:
Height of the building = √1887
Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.
Therefore, the ladder will reach a height of approximately 43.46 meters on the building.
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The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x²
g(x) = ?
A. g(x) = (x - 3)2 + 1
B. g(x) = (x + 3)2 + 1
C. g(x) = (x - 3)2 - 1
O D. g(x) = (x + 3)2 - 1
Answers
The correct answer is A. g(x)=(x-3)^2+1
The equation of the blue graph is g(x) = (x - 3)² + 1.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Since the graphs of f(x) and g(x) intersect at (1.5, 2.5), we can substitute these values into the equations and solve for the constant term:
f(1.5) = g(1.5)
1.5² = g(1.5)
2.25 = g(1.5)
Therefore, we know that the vertex of g(x) is (1.5, 2.25).
Also, since the graphs have the same shape, we know that the vertex of g(x) is obtained by shifting the vertex of f(x) horizontally by the same amount, which is 3 units to the right.
So, the equation of the blue graph can be obtained by replacing x with (x-3) in the equation of the green graph:
g(x) = (x - 3)² + 1
Expanding this equation, we get:
g(x) = x² - 6x + 9 + 1
g(x) = x² - 6x + 10
g(x) = x² - 2 x 3x + 9 + 1
g(x) = (x - 3)² + 1
Therefore,
The equation of the blue graph is g(x) = (x - 3)² + 1.
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Sydney wants to make 15 beaded rings for a craft show. She needs 60 beads for each ring. She has 852 beads. Does Sydney have enough beads to make 15 complete rings?
(She can only make 14 rings I just need to know how many she has leftover)
Answers
Answer:
She actually does have enough beads to make 15 complete rings
Step-by-step explanation:
What is the complementary angle of CFB
Answers
Step-by-step explanation:
CFB reads as twenty five degrees
complementary angle will add to it to sum 90 degrees = sixty five degrees
angle CFD is sixty five degrees
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 15 seats and 22 wheels. The equation representing the total number of seats is u+ b = 15 where u is the number of unicycles and b is the number of bicycles. Select the equation representing the number of wheels. A. 2u+ b = 22 B. u + 2b = 15 C. 2u+b= 15 D. +2b = 22
Answers
The equation representing the number of wheels is u + 2b = 22
The first thing that you need to realize is what slope-intercept form is. Remember that it is y=mx+b. I always say one variable is on the left, while everything else is on the right. After you do that, you need to set up some equations. Seats Each cycle has 1 seat. You know there are 15 seats. So
u+b=15
Manipulate that equation into something that looks like a slope-intercept form.
u+b=15
u+b−b=15−b
u=15−b
unicycle has 1 wheel and a bicycle has 2 and in total there are 22 wheels
u+2b= 22
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PLEASE HELP!!!! Mia has 50 feet of fencing to make a rectangular kennel for her dog. She decides to use part of her hbuse as one side (width)
of the kennel. She needs a minimum enclosed area of 300 square feet. Let/represent the length of the kennel.
Which inequality represent this situation, and what is the solution set?
Select all the correct answers.
Answers
Answer: C and D. Trust me bruh.
Step-by-step explanation:
Answer:
A C D
Step-by-step explanation: Got it correct
Translate the phrase into an algebraic expression.
The product of 9 and x
Answers
The algebraic expression for the product of 9 and x is 9x. This can be expressed in steps as follows:
Step 1: Identify the values that are being multiplied together. In this case it is 9 and x.
Step 2: Write the two values side by side and place a multiplication sign between them.
Step 3: The algebraic expression for the product of 9 and x is then written as 9x.