The proof that at least three of any 25 days chosen must fall in the same month of the year holds true because; there are twelve months in a year.
What is the proof that three of any twenty-five, 25 days chosen must fall in the same month of the year as required in the task content?This proof required for the statement in the task content follows from the fact that, there are 12 months in a year.
here, we have,
Hence, the proof that at least three of any twenty-five, 25 days chosen must fall in the same month of the year is because, there are 12 months in a years and after choosing two days from each month, amounting to 24 days, the 25th day would fall into a month and hence, such month has 3 days already.
Ultimately, the statement that at least three of any 25 days chosen must fall in the same month of the year holds true because there are 12 months in a year.
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Which equation has the solution x = 9? Select each correct answer. Responses 4 + 5x = 18 4 + 5, x, = 18 2x−3=15 2 x minus 3 equals 15 3x + 2 = 25 3, x, + 2 = 25 24−2x=13 24 minus 2 x equals 13 x3+7=8 x over 3 end fraction plus 7 equals 8 81x−3=6 81 over x end fraction minus 3 equals 6
Answer: 2x - 3 = 15 , 81/x - 3 = 6
Step-by-step explanation:
Substitute 9 for x on each equation and see if the sides are equal to each other
4 + 5x = 18
4 + 45 = 18
49 = 18 ( false )
2x - 3 = 15
2(9) - 3 = 15
18 - 3 = 15
15 = 15
3x + 2 = 25
3(9) + 2 = 25
27 + 2 = 25
29 = 25 ( false )
24 - 2x = 13
24 - 2(9) = 13
24 - 18 = 13
6 = 13 ( false )
x/3 + 7 = 8
9/3 + 7 = 8
3 + 7 = 8
10 = 8 ( false )
81/x - 3 = 6
81/9 - 3 = 6
9 - 3 = 6
6 = 6
Hope this helps !
helphelphelphelp
i need help quick
whoever answers this first..
i will give them 100 points
Answer:
Decreased by 19%.
-------------------------------
Decrease by of x 10% can be shown as a product of x and:
100% - 10% = 90% = 0.9Same applies to the second decrease, then we get a final number:
x*0.9*0.9 = 0.81 xIt represent a one off decrease of:
1 - 0.81 = 0.19 = 19%Hence the answer is 19%.
Answer:
19%
Step-by-step explanation:
let's start from 100 and remove 10%100 - 100/10 = 90
let's take 10% off again90 - 90/10 = 91
find the difference between 100 and 81100 - 81 = 19%
for a better understanding look at the figure
Please help find the radius, circumference, and area
What is the y-intercept when the coordinate is 9,1 and the slope is 4 8
Answer:
the formula for this is y=mx+b
b stands for the y, m is the slope of the line, and x stands for the x axis!
Step-by-step explanation:
i am pretty sure your answer is -1.4
hope this helps I to help you out attached a screenshot
Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the shaded region.
The x y coordinate plane is given. There are two curves, two horizontal lines, and a shaded region on the graph.
The first curve, labeled x = y2 − 5, enters the window in the fourth quadrant, goes up and left becoming more steep, crosses the y-axis at approximately y = −2.2, changes direction at the point (−5, 0), goes up and right becoming less steep, crosses the y-axis at approximately y = 2.2, and exits the window in the first quadrant.
The second curve, labeled x = ey, enters the window almost vertically just right of the y-axis, goes up and right becoming less steep, crosses the first curve just right of the y-axis at approximately y = −2.3, crosses the x-axis at x = 1, and exits the window in the first quadrant.
The first horizontal line, labeled y = −1, begins at the point (−4, −1) on the first curve, goes right, and ends at the approximate point (0.4, −1) on the second curve.
The second horizontal line, labeled y = 1, begins at the point (−4, 1) on the first curve, goes right, and ends at the approximate point (2.7, 1) on the second curve.
The region is right of the first curve, left of the second curve, above the first horizontal line, and below the second horizontal line.
Refer to the image attached.
In 2012, the cost of a hamburger at a famous nationwide restaurant chain was $4.32. In 2022 the
price of the same hamburger is $6.12.
a. What is the average rate of change in the cost of the hamburger during this period?
b. Using the price in 2012 as an initial value, write a linear equation that models the cost of
the hamburger.
c. Using the model from part b, when will the price of the hamburger reach $7.02?
Answer:
Step-by-step explanation:
a. The average rate of change in the cost of the hamburger during the period from 2012 to 2022 can be calculated as the difference in the cost of the hamburger divided by the number of years between the two prices.
So, the average rate of change in the cost of the hamburger is:
(6.12 - 4.32) / (2022 - 2012) = 0.18
Therefore, the average rate of change in the cost of the hamburger during this period is $0.18 per year.
b. We can use the point-slope form of a linear equation to model the cost of the hamburger as it changes over time. Let y be the cost of the hamburger in dollars, and t be the number of years since 2012. We know that the cost of the hamburger in 2012 was $4.32, so we have a starting point of (0, 4.32).
Using the average rate of change calculated in part a, we can find the slope of the line:
slope = (6.12 - 4.32) / (2022 - 2012) = 0.18
Now we can write the equation of the line as:
y - 4.32 = 0.18t
y = 0.18t + 4.32
So, the linear equation that models the cost of the hamburger in terms of years since 2012 is y = 0.18t + 4.32.
c. To find when the cost of the hamburger will reach $7.02, we can substitute y = 7.02 into the equation we found in part b and solve for t:
7.02 = 0.18t + 4.32
2.7 = 0.18t
t = 15
So, the cost of the hamburger will reach $7.02 in the year 2012 + 15 = 2027.
A ring-shaped region is shown below. Its inner radius is 11 m. The width of the ring is 3 m. 11 m Find the area of the shaded region. Use 3.14 for л. Do not round your answer.
The area of the shaded region is 235.5 m².
What is the area of the shaded region?To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle.
The outer radius of the ring can be found by adding the width of the ring to the inner radius:
Outer radius = inner radius + width
= 11 m + 3 m
= 14 m
The area of a circle is given by the formula:
Area = π × (radius)²
Therefore, the area of the inner circle is:
Area of inner circle = π × (11 m)²
= 121π m²
And the area of the outer circle is:
Area of outer circle = π × (14 m)²
= 196π m²
To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle:
Area of shaded region = Area of outer circle - Area of inner circle
= 196π m² - 121π m²
= 75π m²
= 75 x 3.14
= 235.5 m²
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Simplify the expression. 4+5/3^2−2^
2
The simplified expression is 25/9, of the given expression. 4 + (5/3)² − 2².
What is the exponentiation?
An exponential function is a mathematical function of the following form: f (x) = ax. where x is variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately
To simplify the expression, we need to follow the order of operations, which is:
Evaluate any expressions inside parentheses or brackets.
Exponents (ie, powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order, we can simplify the expression as follows:
4 + (5/3)² - 2²
= 4 + (25/9) - 4 ..........5/3 squared is 25/9 and 2 squared is 4
= (36/9) + (25/9) - (36/9) ..........rewrite 4 as 36/9 to have a common denominator of 9
= 25/9
Therefore, the simplified expression is 25/9.
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The value went from $45.00 to $68.75. What was the percent change?
The percent change from $45.00 to $68.75 is approximately 52.8%.
What does the phrase "percent change" mean?Finding the difference between two values in a time series and multiplying it by 100 after dividing it by the initial value yields the percentage change between the two values.
We employ the following formula to determine the percentage difference between two values:
(New Value - Old Value) / Old Value * 100% is the formula for percent change.
The former value in this instance was $45.00, whereas the new value is $68.75.
Adding these values to the formula yields the following results:
($68.75 - $45.00) / $45.00 * 100% is the percent difference.
percent modification: (23.75% / (45.00%) * 100%
52.8% change in percentage
As a result, the percentage increase from $45.00 to $68.75 is almost 52.8%.
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Alfonso Inc. acquired 100 percent of the voting shares of BelAire Company on January 1, 2020. In exchange, Alfonso paid $387,500 in cash and issued 100,000 shares of its own $1 par value common stock. On this date, Alfonso’s stock had a fair value of $15 per share. The combination is a statutory merger with BelAire subsequently dissolved as a legal corporation. BelAire’s assets and liabilities are assigned to a new reporting unit.
Answer:
This scenario describes a business combination in which Alfonso Inc. acquired 100% ownership of BelAire Company on January 1, 2020, using both cash and common stock as consideration. The combination is a statutory merger, meaning that BelAire is dissolved as a legal corporation and its assets and liabilities are assigned to a new reporting unit.
To record this business combination, Alfonso would need to perform a detailed analysis of the fair values of the assets and liabilities of BelAire as of the acquisition date, and allocate the total consideration paid (i.e., $387,500 in cash plus the fair value of 100,000 shares of Alfonso's common stock) to those assets and liabilities based on their fair values.
Assuming that the fair values of the assets and liabilities of BelAire on the acquisition date were as follows:
Assets:
Cash: $50,000
Accounts receivable: $100,000
Inventory: $150,000
Property, plant, and equipment: $400,000
Goodwill: $200,000
Liabilities:
Accounts payable: $75,000
Long-term debt: $250,000
The total fair value of BelAire's net assets is ($50,000 + $100,000 + $150,000 + $400,000 + $200,000) - ($75,000 + $250,000) = $575,000.
The allocation of the consideration paid would be as follows:
Cash paid: $387,500
Fair value of 100,000 shares of Alfonso's common stock: 100,000 shares x $15 per share = $1,500,000
Total consideration paid: $1,887,500
Allocation of consideration:
Cash: $50,000 / $575,000 x $1,887,500 = $164,348
Accounts receivable: $100,000 / $575,000 x $1,887,500 = $328,261
Inventory: $150,000 / $575,000 x $1,887,500 = $492,174
Property, plant, and equipment: $400,000 / $575,000 x $1,887,500 = $1,310,870
Goodwill: $200,000 / $575,000 x $1,887,500 = $657,391
Accounts payable: $75,000 / $575,000 x $1,887,500 = $246,739
Long-term debt: $250,000 / $575,000 x $1,887,500 = $818,478
The entry to record the acquisition would be:
Debit Property, plant, and equipment: $1,310,870
Debit Goodwill: $657,391
Debit Cash: $164,348
Debit Accounts receivable: $328,261
Debit Inventory: $492,174
Credit Accounts payable: $246,739
Credit Long-term debt: $818,478
Credit Cash: $387,500
Credit Common stock: $1,500,000
This entry records the allocation of the total consideration paid to the assets and liabilities acquired, as well as the issuance of Alfonso's common stock to BelAire's shareholders.
The graph below is the function f(x)
The correct statements regarding the function are given as follows:
f(2) is defined.The function is not continuous at x = 2.What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
To the left of x = 2, the graph of the function approaches x = 2 at y = 2, hence:
lim x-> 2^- f(x) = 2.
To the right of x = 2, the graph of the function approaches x = 2 at y = 1, hence:
lim x-> 2^+ f(x) = 1.
Due to the different lateral limits, the function is not continuous at x = 2, and the limit is not defined.
Due to the closed circle, the function is defined at x = 2, with a numeric value of y = 2.
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Find the area of the parallelogram.
Answer:
30 cm²
Step-by-step explanation:
The formula to find the area of a parallelogram.
Area = Base × Height
Accordingly, let us find the area.
Area = Base × Height
Area = 10 cm × 3 cm
Area = 30 cm²
Solve for the roots in simplest form using the quadratic formula: 4x^2+21=-20x
The roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are x = -1/2 and x = -7/2.
What is quadratic formula ?
The quadratic formula is a standard formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is derived using the method of completing the square and provides a simple way to find the roots (or solutions) of the quadratic equation.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
Steps to be followed:
To solve the quadratic equation 4x^2 + 21 = -20x using the quadratic formula, we first need to rearrange the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, we have:
4x^2 + 20x + 21 = 0
So, we can identify a = 4, b = 20, and c = 21. Now we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values of a, b, and c, we get:
x = (-20 ± √(20^2 - 4(4)(21))) / 2(4)
Simplifying the expression under the square root, we get:
x = (-20 ± √(400 - 336)) / 8
x = (-20 ± √64) / 8
x = (-20 ± 8) / 8
This gives us two possible solutions:
x = (-20 + 8) / 8 = -1/2
x = (-20 - 8) / 8 = -7/2
Therefore, the roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are x = -1/2 and x = -7/2.
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You pick a card at random. 4 5 6 7 8 What is P(not prime)?
the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
How we solved?
To determine the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8}, we first need to identify which numbers in the set are prime.
The prime numbers in the set are 5 and 7, so the non-prime numbers are 4, 6, and 8.
The total number of cards in the set is 5.
Therefore, the probability of selecting a non-prime card is:
P(not prime) = number of non-prime cards / total number of cards
P(not prime) = 3 / 5
P(not prime) = 0.6 or 60%
So the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.
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pls help asap pls i pay 54
The value of BC is 9cm.
What is a similar triangle?
If two triangles have the same shape or have the same shape as their mirror images, they are said to be comparable. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
Here, we have
Given: BA = 6cm, AC = 8cm
BC =?
In a similar triangle, their side is also proportional.
BA/ED = AC/DF = BC/EF
BA/ED = BC/EF
6/18 = BC/27
18BC = 6×27
BC = 6×27/18
BC = 9cm
Hence, the value of BC is 9cm.
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7/17.5 cm=12/x what is x
We receive the ratio as follows:
7/17.5 = 12/x
We can cross-multiply and solve for x to determine x:
7x = 17.5 × 12
7x = 210
x = 210/7
x = 30
Hence, x has a value of 30 cm.
What are measurements?Measuring is a method that involves comparing an object's characteristics to a reference value to ascertain its attributes. The primary metric for expressing any quantity of items, things, and occurrences is measurement.
Measuring MethodsIn a number of branches of mathematics, we work with several fundamental categories of measurement variables. As follows:
Time Length Weight Volume TemperatureThe fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently. Also, in that, it requires a specific number of items to complete a specific task. We frequently encounter many measurements kinds for length, weight, times, etc. in our daily lives.
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Angles A and C are supplementary. Find the measure of angle C.
Angle EAB is 74 degrees. Angle FCD is undetermined.
How do I solve this problem?
In the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles.
For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary.
We say two angles "Complement" one other when their sums equal 90 degrees.
So, we already are aware of that:
∠A and ∠C are supplementary
∠A is 74°
Then, ∠C would be:
∠A + ∠C = 180
74 + ∠C = 180
∠C = 180 - 74
∠C = 106
Therefore, in the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.
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Correct question:
Angles A and C are supplementary. Find the measure of angle C.
(Refer to the image below)
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
The key features of this rational function include the following:
Domain: (-∞, 1) ∪ (1, ∞)
Range: (-∞, 3) ∪ (3, ∞)
Y-intercept: -5.
X-intercept: 5/3.
Vertical asymptote: x = 1.
Horizontal asymptote: y = -3.
What is a rational function?In Mathematics, a rational function simply refers to a type of function which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:
NumeratorDenominatorIn order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.
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- Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
The cosine function that would model the tide situation for this beach is given as follows:
y = -3cos(πx/12) + 1.
How to define the cosine function?The function is at it's minimum value at the origin, hence it is a reflected cosine function, defined as follows:
y = -Acos(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C is the vertical shift.The minimum value is of -2, while the maximum value is of 4, for a difference of 6, hence the amplitude of the function is given as follows:
2A = 6
A = 6/2
A = 3.
With no vertical shift, the function should oscillate between -A = -3 and A = 3, but it oscillates between -2 and 4, hence the vertical shift is given as follows:
C = 1.
The period is of 24 hours, hence the coefficient B is given as follows:
2π/B = 24
24B = 2π
B = π/12.
Hence the function is defined as follows:
y = -3cos(πx/12) + 1.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Using the arithmetic operation the value for x in the equation (x – 7)2 = 36 is obtained as 25.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is (x – 7)2 = 36.
Use the arithmetic operation of multiplication -
2x - 14 = 36
Collect all the like terms -
2x = 36 + 14
Use the arithmetic operation of addition -
2x = 50
Use the arithmetic operation of division -
x = 50/2
x = 25
Therefore, the value is 25.
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If p - r = 11 and q - r = -5, what is the value of p - q? -16 -6 6 16
The value of the expression P-q will be 16. The correct option is C.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
To find the value of p - q, we need to eliminate r from the two equations given to us.
We can do this by solving for r in one of the equations and then substituting that expression into the other equation.
Let's solve for r in the equation p - r = 11:
r = p - 11
Now we can substitute this expression for r into the equation q - r = -5:
q - (p - 11) = -5
Simplifying this equation by distributing the negative sign, we get:
q - p + 11 = -5
Subtracting 11 from both sides, we get:
q - p = -16
Therefore, p - q = -(q - p) = -(-16) = 16.
So the answer is 16.
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1/2 x^2 +. 1 =0
solve each equation by graphing related function
Answer:
Step-by-step explanation:
Math Word Problem: A farmer had some chickens and some cows. She counted 40 heads and 126 legs. How many chickens and how many cows did she have? Show your work.
Answer:
There are 17 chickens and 23 cows
Step-by-step explanation:
Assuming every chicken has 1 head and 2 legs and every cow has 1 head and 4 legs, let us set up a system of equations for this proble
Let
x = number of chickens
y = number of cows
x chickens will have x heads
y cows will have y heads
Total number of heads = x + y = 40
x chickens will have 2x legs
y cows will have 4y legs
Total legs = 2x + 4y = 126
We have two equations:
x + y = 40 (1)
2x + 4y = 126 (2)
Multiply: (1) x 2
=> 2(x + y) = 2(40)
=> 2x + 2y = 80 (3)
Subtract: (2) - (3)
2x + 4y - (2x + 2y) = 126 - 80
2x + 4y -2x - 2y = 46
4y - 2y = 46
2y = 46
y = 23
Since y = 23 and x + y = 40
x + 23 = 40
x = 40 - 23 = 17
There are 17 chickens and 23 cows
HELPPPPP
can someone give me the answer for this
Answer:
x = -1, y = 1
Step-by-step explanation:
2x - 3y = -5
3x + y = -2
2x - 3y = -5
9x + 3y = -6
11x = -11
x = -1
-3 + y = -2
y = 1
x = -1, y = 1
What is the volume of this figure?
Answer: 186 cubic in
Step-by-step explanation:
The number of people who survived the Titanic based on class and gender is in the table below. Suppose a person is picked at random from the survivors. Female Male Total 193 1st 134 59 2nd 194 25 119 3rd 80 58 138 Total 308 142 450 a) What is the probability that a survivor was male? b) What is the probability that a survivor was in the 2nd class? c) What is the probability that a survivor was a male, given that the person was in the 2nd class? d) What is the probability that a survivor was a male and in the 2nd class? e) What is the probability that a survivor was a male or in the 2nd class?
a) The probability that a survivor was male is:
142/450 = 0.315
b) The probability that a survivor was in the 2nd class is:
119/450 = 0.264
c) The probability that a survivor was a male, given that the person was in the 2nd class is:
25/119 ≈ 0.210
d) The probability that a survivor was a male and in the 2nd class is:
25/450 ≈ 0.056
e) The probability that a survivor was a male or in the 2nd class is:
P(male or 2nd class) = P(male) + P(2nd class) - P(male and 2nd class)
= 142/450 + 119/450 - 25/450
= 236/450
= 0.524
Which expression has the same value as (8 x 5) + (8 × 3) ?
A.8x8
B.8 x 15
C.16 + 8
16+8
D 13+11
Mrs. Smith has 310 pencils in her classroom. Each student gets 3³
pencils. How many students are in her class? Leave your answer in
exponent form.
A. 313
B. 330
C. 37
D. 39
The number of students in mrs. Smith's class in exponent form is 3⁷.
How many students are in Mrs. Smith class?Given that, Mrs. Smith has 3¹⁰ pencils in her classroom. Each student gets 3³ pencils.
Let the number of students in the class be represented by n.
Total number of pencils = 3¹⁰Number of pencils each student gets = 3³Number of students in the class = nTo get the number of students in the class, divide the total number of pencils by the number of pencils each student got.
n = Total number of pencils ÷ Number of pencils each student gets
n = 3¹⁰ ÷ 3³
Since they both have the same base, we subtract the exponents
n = 3¹⁰ ⁻ ³
n = 3⁷
Therefore, the number of students is 3⁷.
Option D) 3⁷ is the correct answer.
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Explain why the discriminant affects the type of roots for a quadratic equation
Answer:
See below
Step-by-step explanation:
The roots aka solutions to a quadratic equation in standard form:
[tex]ax^2 + bx + c = 0[/tex]
are given by
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
The term under the square root sign, [tex]b^2 - 4ac[/tex] is called the discriminant
The type and number of roots are determined by the sign of the discriminant
When [tex]b^2 - 4ac = 0[/tex] there is one real root.
When [tex]b^2 - 4ac > 0[/tex] there are two real roots.
When [tex]b^2 - 4ac < 0[/tex] there are two complex(imaginary) roots.
Which of the following equations has no real solutions?
OA. 10(x-6) = 10x - 60
OB.10(x+6)= 10(x + 10)
OC. 10x-6=60x-6
OD. 10x-610x6
Answer:
10x-610x6
The equation 10x-610x6 has no real solutions because it cannot be solved for any value of x. The left side of the equation is 10x-6, and the right side is 10x+6. Since the left side is greater than the right side, no value of x can make the equation true.