Answer:
6-y^2 can be factored by using the difference of squares formula which states that:
a^2 - b^2 = (a+b)(a-b)
We can factorize 6-y^2 by using the following:
6 - y^2 = (sqrt(6) + sqrt(-y^2))(sqrt(6) - sqrt(-y^2))
= (sqrt(6) + yi)(sqrt(6) - yi)
where i is the imaginary unit.
So, 6-y^2 = (sqrt(6) + yi)(sqrt(6) - yi) is the factored form of 6-y^2
Please note that the factorization is only true for real values of y, when y is not real the expression can't be factorized.
which expression evaluates to true if and only if the units digit of an integer variable x is less than 6
The units digit of an integer every square of an integer ends with (=has a units digit) 0, 1, 4, 5, 6, or 9.
This question can be answered in a variety of ways. Finding squares with the unit digits 0, 4, 5, and 6 is one way to demonstrate by means of elimination that the answer must be 2. The reason this method works is that you're presuming one of the answers to this specific multiple-choice question is true, but it's not actually that fulfilling.
A more effective method is to note that any number has the form (10m+i) such that 0i9. By squaring, you may determine exactly which numbers are feasible units digits in a square by getting 100m2+20mi+i2, etc. in turn.
Every square of an integer should have the units digit (0, 1, 4, 5, 6, or 9) as its final value.
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If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?1/54/5516
The constant of variation for this relation will be option (C.) 5
Constant of variationThe ratio between two variables in a direct variation or the product of two variables in an inverse variation.
We solve the problem as follows.
Given that y is directly proportional x
y = kx, where k = proportionality constant
Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.
According to the provided data,
y = 20
x = 4.
So,
20 = 4k
k = 20/4 = 5
Therefore constant of variation will be 5
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Which of the following cannot be the sides of a triangle?
(i) 4.5 cm, 3.5 cm, 6.4 cm
(ii) 2.5 cm, 3.5 cm, 6.0 cm
(iii) 2.5 cm, 4.2 cm, 8 cm
(ii) 2.5 cm, 3.5 cm, 6.0 cm and (iii) 2.5 cm, 4.2 cm, 8 cm cannot be the sides of a triangle.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
(i) 4.5 cm, 3.5 cm, 6.4 cm
4.5 + 3.5 = 8 > 6.4
4.5 + 6.4 =10.9 > 3.5
3.5 + 6.4 = 9.9 > 4.5
so these lengths can form a triangle.
(ii) 2.5 cm, 3.5 cm, 6.0 cm
2.5 + 3.5 = 6.0 = 6.0
2.5 + 6.0 = 8.5 > 3.5
3.5 + 6.0 = 9.5 > 2.5
so these lengths cannot form a triangle.
(iii) 2.5 cm, 4.2 cm, 8 cm:
2.5 + 4.2 = 6.7 < 8
2.5 + 8 = 10.5 > 4.2
4.2 + 8 = 12.2 > 2.5
so these lengths cannot form a triangle.
Therefore, (ii) and (iii) cannot be the sides of a triangle.
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Find the equation of the linear function represented by the table below in
slope-intercept form.
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
we see that with every increase of x by 1 y increases by 3.
so, the slope "a" is 3.
to get b we use one of the given points, e.g. (1, 5) :
5 = 3×1 + b = 3 + b
b = 2
so, our function is
y = 3x + 2
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer to Problem 13 is 34.5
Answer to Problem 15 is 22.9
==================================================
Work Shown for Problem 13
sin(x)/17 = sin(91)/30
sin(x) = 17*sin(91)/30
sin(x) = 0.56658036
x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)
x = 34.51210645 or x = 180-34.51210645
x = 34.51210645 or x = 145.48789355
x = 34.5 or x = 145.5
If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).
If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)
In short, x = 34.5 is valid while x = 145.5 is not valid.
Therefore, the only possible answer is 34.5
---------------------------------------------
Work Shown for Problem 15
sin(x)/20 = sin(119)/45
sin(x) = 20*sin(119)/45
sin(x) = 0.38871987
x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)
x = 22.87486940 or x = 180-22.87486940
x = 22.87486940 or x = 157.1251306
x = 22.9 or x = 157.1
If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.
If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1
The only possible answer is therefore 22.9
---------------------------------------------
Side notes:
Make sure your calculator is in degree mode. Unfortunately some calculators like to default to radian mode. A quick check is to see if sin(30) produces the result 0.5Arcsine is the same as inverse sine, which is denoted as [tex]\sin^{-1}[/tex] on many calculators.The manager at Apex Gym wants to know when the new pricing model (higher per-class fee but lower membership fee) will be better than the old pricing model used last year. He uses a table to calculate the members’ costs for different numbers of classes.
The completed table to show the member cost for different numbers of classes is :
No. of classes Cost under old model Cost under new model
2 170 110
4 200 170
5 215 200
6 230 230
7 245 260
How to find the member costs ?Assuming that the number of classes is x, then the formula to find the cost with a certain number of classes with the old model is:
= 15 x + 140 membership fee
4 classes :
= 15 x 4 + 140
= $ 200
5 classes :
= 15 x 5 + 140
= $ 215
6 classes :
= 15 x 6 + 140
= $ 230
7 classes :
= 15 x 7 + 140
= $ 245
Cost under new model would take the formula:
= 30 x + 50 membership fee
4 classes :
= 30 x 4 + 50
= $ 170
5 classes :
= 30 x 5 + 50
= $ 200
6 classes :
= 30 x 6 + 50
= $ 230
7 classes :
= 30 x 7 + 50
= $ 260
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Sam has a goal of walking (3)1/2 miles by the end of the day. He walks (1)1/8 miles before lunch and 3/4 miles after resting. What is the remaining distance, in miles, that same needs to walk to reach his goal?
Since the remaining distance is negative, it implies that Sam has already exceeded his goal distance. Therefore, he doesn't need to walk any further to reach his goal.
To find the remaining distance that Sam needs to walk to reach his goal of (3)1/2 miles, we need to subtract the distance he has already walked from his goal distance.
Sam walks (1)1/8 miles before lunch and 3/4 miles after resting. To calculate the total distance he has walked, we add these two distances:
Total distance walked = (1)1/8 + 3/4
To add these fractions, we need to find a common denominator, which is 8 in this case
Total distance walked = (9/8) + (6/8)
= 15/8
= 1 (7/8)
Now, we subtract the total distance walked from Sam's goal distance:
Remaining distance = (3)1/2 - 1 (7/8)
To subtract fractions, we also need a common denominator. The common denominator is 2 in this case:
Remaining distance = (6/2 + 1/2) - (15/8)
= (12/8 + 1/8) - (15/8)
= 13/8 - 15/8
= -2/8
= -1/4
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two cards are selected with replacement from a standard deck of 52 cards. find the probability of selecting a spade and then selecting a heart.
The probability of selecting a spade and then selecting a heart from a standard deck with replacement is 0.625.
When selecting two cards with replacement from a standard deck of 52 cards, the probability of selecting a specific card on the first draw does not affect the probability of selecting a specific card on the second draw. Therefore, we can simply multiply the probability of selecting one card of a specific suit by the probability of selecting a different card of a specific suit.
The probability of selecting a spade on the first draw is
13/52 = 1/4 = 0.25
since there are 13 spades in a deck of 52 cards.
The probability of selecting a heart on the second draw is also
13/52 = 1/4 = 0.25
since there are 13 hearts in a deck of 52 cards.
Therefore, the probability of selecting a spade and then selecting a heart is:
(0.25) * (0.25) = 0.0625
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An instructor wants to write a quiz with 9 questions where each question is worth 3, 4, or 5 points based on difficulty. he wants the number of 3-point questions to be 1 more than the number of 5-point questions, and he wants the quiz to be worth a total of 35 points. determine the number of 3-point, 4-point, and 5-point questions.
The quiz should have 5 3-point number of questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.
3-point questions: 5
4-point questions: 3
5-point questions: 4
1. The total number of questions is 9.
2. The total number of points for the quiz is 35.
3. There should be 1 more 3-point question than 5-point questions.
4. So, 5 of the questions should be worth 3 points each, for a total of 15 points.
5. That leaves 4 points remaining.
6. 4 points can be achieved by having 3 4-point questions (12 points) and 4 5-point questions (20 points).
7. Therefore, the number of 3-point, 4-point, and 5-point questions should be 5, 3, and 4 respectively.
The quiz should have 5 3-point questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.
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a cyclist rides at a average speed of 18km/h for 9 minuets. work out the distance traveled by the cyclist in km
Answer: d=162km
Step-by-step explanation:
the equation of this question is:
speed = distance / time
s=d/t
18=d/9
d=18*9
d=162km
Helpppppppppppppp meeeeeeeee plssssssssss
By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)
How to determine the simplified form of a rational equation
In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:
1 / [1 / (x + 2) + 1 / (x + 3)]
Second, expand the denominator by addition of fractions with distinct denominator:
1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]
Third, use division of fractions:
[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]
Fourth, simplify both numerator and denominator:
(x² + 5 · x + 6) / (2 · x + 5)
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In 1997, a city had a population of 220,000 people. Each year since, the population has grown by 6.2%.
Let t be the number of years since 1997. Let y be the city’s population.
Write an exponential function showing the relationship between y and t.
The exponential function that shows the relationship between y and t is y = 220,000(1.062^t).
What is the exponential function?An exponential equation can be described as an equation with exponents. The exponent is usually a variable.
The general form of exponential equation is f(x) = e^x
Where:
x = the variable e = constantThe form of the exponential equation that can be used to determine the population after 1997 is:
FV = P (1 + r)^n
Where:
FV = future population P = present population R = growth rateN = number of yearsy=220,000 x ( 1+ 0.062)^t
y = 220,000(1.062^t).
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Solve for X, Leave in simplest radical form.
The value of x (hypotenuse) by using trigonometry is 2√5.
What is trigonometry ?
The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.
The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.
In the triangle height = √15 and hypotenuse as x
The value of the angle is 60°
by using trigonomtry we can write
sin60° = height/ hypotenuse
√3/2 = √15/ x
x = (√15 * 2)/√3
x = 2√5
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Select the correct description for the quadratic expression below
the product of x and a factor not depending on x
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation given 3x(m-6n)²
This expression contains two factors:
1 factor: 3x
2 factor: (m-6n)²
Hence the product of x and a factor not depending on x.
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How do you solve absolute value Grade 7?
In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.
Here is a step-by-step process to solve an absolute value equation:
Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.
For example, |x| = 3 can be rewritten as x = 3 or x = -3
Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.
Solve each case separately.
Check your solutions by plugging them back into the original equation and making sure they are valid solutions.
Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.
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pencils come in packages of 18. erasers come in packages of 12. phillip wants to have the same number of pencils as erasers. how many packs of pencils and how many packs of eraser will he have to buy?
By applying the Least Common Multiple theory, it can be concluded that Philip has to buy 2 packs of pencils and 3 packs of erasers.
Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that could be divided by those numbers.
The simplest way to find the LCM of two or more numbers is to list the multiples of each number.
Then, check the smallest multiple that appears in all of the multiple lists. This value is the LCM of those numbers.
From the question, we know that Philip wants to have the same number of pencils as erasers. Whilst they come in different packages. To do so, firstly we list the multiples of each package.
Pencil: 18 : 18, 36, 54, 72, 90, ...
Eraser: 12 : 12, 24, 36, 48, 60, ...
Now we check the smallest multiple that appears in all of the multiple lists, the LCM is 36.
36 pencils means 36 : 18 = 2 packs of pencils
36 erasers means 36 : 12 = 3 packs of erasers
Thus, Philip has to buy 2 packs of pencils and 3 packs of erasers
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Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answer: [tex]4x^4 -3x^3 y+8x^2 y^2 -7xy^3[/tex]
Step-by-step explanation:
In standard form, the terms are arranged in order from highest to lowest exponent of the variable that comes first alphabetically.
A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term
The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.
A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.
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the random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution?
The random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution:
X ~ Exp( μ = 53)
Random Variable:
A random variable is a variable that can take many values. This is because random events can have multiple outcomes. So don't confuse random variables with algebraic variables. Algebraic variables represent the values of unknown quantities in computable algebraic equations. A random variable, on the other hand, can have a range of values that could be the result of a random experiment.
Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X is 2 (1 + 1) and the maximum value is 12 (6 + 6). Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.
According to the Question:
We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:
X ~ Exp( μ = 53)
But, also we can define the variable in terms of like this:
X ~ Exp (λ =1/λ =1/53)
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A circle centered at $P$ with radius $10$ and a circle centered at $Q$ with radius $8$ are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$
If the two circle centered at P and Q with radius 10 and 8 respectively , and if the common external tangent intersects line PQ at R , then the length of QR is 72 .
The radius of the circle that is centered at P is = 10 ;
the radius of circle that is centered at Q is = 8 ;
the common external tangent intersects the line PQ at R ,
Let XYR be external tangent with X on the Circle with center P , and at point Y on circle with center Q .
we extend , the line PQ to point R ,
we get , that triangle XPR is similar to triangle YQR ,
it means that , [tex]\frac{RQ}{RP} =\frac{QY}{PX}[/tex] ;
let the length of RQ be = x , then
length of RP will be = [tex]x+18[/tex] ;
we get ; [tex]\frac{x}{x+18} =\frac{8}{10}[/tex] ;
⇒ [tex]10x=8x+144[/tex] ;
⇒ [tex]2x=144[/tex] ;
⇒ [tex]x=72[/tex] .
Therefore , the length of QR is 72 .
The given question is incomplete , the complete question is
A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR .
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Can a triangle have sides with 8 cm 7 cm and 9 cm?
Yes, for the given measurement of sides 8cm , 7cm, and 9cm the triangle formation is possible as sum of two sides is always greater than the third side.
As given in the question,
Given measurement of the side length of the triangle is equal to :
Measurement of Side 1 = 8cm
Measurement of Side 2= 7cm
Measurement of Side3 = 9cm
To form a triangle sum of the measure of two sides of a triangle should be greater than the measure of the third side of the triangle.
In the given triangle,
Side 1 + Side 2
= 8cm + 7cm
= 15cm > 9cm
Side 1 + Side 3
= 8cm + 9cm
= 17cm > 7cm
Side 3 + Side 2
= 9cm + 7cm
= 16cm > 8cm
Therefore, sum of measure of two sides is always greater than the third side it is possible to form a triangle with given measurement of sides.
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when canned peaches are delivered to a grocery store, the clerk stocks the new cans in front of the old. if each can sold is accounted for as to its cost, a) lifo (last-in, first-out). b) average. c) random. d) fifo (first-in, first-out).
According to the given statement If each can sold in accounted for as to its cost Last in first out.
Why do we determine the average?The average is determined by adding together all of the numbers as well as dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value. We constantly encounter the average computation in our daily lives.
Which 4 averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or dispersion.
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Find the value of x, if it has a value:-
[tex]\tt 33-5(x-4)=3[/tex]
Step-by-step explanation:
[tex]\tt 33-5(x-4)=3[/tex]
[tex]\tt 33-5x+20=3[/tex]
[tex]\tt 53-5x=3[/tex]
[tex]\tt -5x=3-53[/tex]
[tex]\tt 5x=50[/tex]
[tex]\tt x=10[/tex]
I hope it's helpful
Consider the following expression. 8y+3x+5 Select all of the true statements below.
All of the true statements that have to do with the expression 8y+3x+5 are:
5 is a constant3x + 8y + 5 is written as a sum of three terms3x and 5 are like termsWhat is a mathematical expression?An expression in mathematics is made up of a mixture of variables, integers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
In the equation 5 is a constant, this is because the value would not have to change because it does not have a variable attached.
The terms of the expression are, 3x, 8 y and 5. This makes it a total of 3 terms in the expression.
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Given that 2 cos x = √3, where 0° < x < 90°,
find the value of x.
Answer:
30 degrees.
Step-by-step explanation:
2 cos x = √3
cos x = √3/2
x = 30.
over a period of one year, two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart. what is this distance, in meters? (1 meter
As per the given points, the distance is 0.08 meter.
The term distance in math is known as the length of the line joining the two points.
Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.
Here we have to calculate the distance between the two point in meter.
Let us consider that x be the distance between the two points.
As we know that in each side there is 4 centimeter distance.
Then the total distance between the two points,
=> 4 x 2 = 8 centimeter.
Then the meter equivalent is calculated as,
=> 8/100 = 0.08
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Complete the equation describing how x
and y are related.
X y
7
9
11_ y = [ ? ]x +
13
15
17
012345
Enter the answer that
belongs in [?].
Enter
Help
Skip
The complete equation is y =2x+7 after substituting the given values.
What is equation?
An equation is a condition on a variable such that two expressions in the variable should have equal value and Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
y = ax+b
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
7 = a(0) + b
b= 7
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
9 = a(1)+b
9 = a+7
a=9-7
a=2
substitute the value of a and b in the equation y = ax + b. we get ,
y = 2x+7
Therefore, the complete equation is y = 2x+7
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If 21x^3-42x² + 3x is divided by 3x, the quotient is
The quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.
What is quotient?When we divide a number, the result we ultimately get is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally divided. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.
The given expression is:
21x^3 - 42x^2 + 3x
Divide the equation by 3x:
21x^3 - 42x^2 + 3x / 3x
Divide each term with 3x.
Using the rule of exponents we have a^n/ a^m = a^(n-m):
7x^2 - 14x + 3
Hence the quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.
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hope runs a pizza restaurant. she must pay $70 to keep the restaurant open each day even if she does not sell any pizza. additionally, each slice of pizza that she makes and sells costs her $0.6. write a formula for the function c ( x ) that expresses hope's total daily costs as a function of the number of slices x that she makes/sells.
How many 1/4 are in 3
Answer:
there are 12 fourths in 3 .
