Answers
Answer:
The Domain D = {y ∈ R / y ≠ [tex]\dfrac{b}{2}[/tex] y ≠ 0}
Step-by-step explanation:
Let ,
f(y) = [tex]\dfrac{b^{2} - 4by }{2y^{2} - by }[/tex] - [tex]\dfrac{4y}{b-2y}[/tex]
The above function would be defined only when the denominator of anyone or both the terms of the function do not become 0 -
[tex]2y^{2} - by[/tex] ≠ 0 and b - 2y ≠ 0
∴ y(2y - b) ≠ 0 and y ≠[tex]\dfrac{b}{2}[/tex]
Either y ≠ 0 or y ≠ [tex]\dfrac{b}{2}[/tex]
∵ The domain of a function consists of only those points where the function is defined -
The Domain D consists of all y ∈ Real numbers such that y ≠ 0 and y ≠ [tex]\dfrac{b}{2}[/tex]
Related Questions
Which ordered pair would form a proportional relationship with the point graphed below?
(10, –20)
(–30, 20)
(–10, 5)
(35, –20)
Answers
Answer:
I think it would be either (-10, 5) or (35, -20)
Step-by-step explanation:
Answer:
It Is C
Step-by-step explanation:
Edg 2020
How many solutions does this system of equations have?
exactly one
exactly two
infinitely many
none
Answers
Answer:
exactly one
Step-by-step explanation:
1. subtract 2x from the equation 2x + y = 1
2. now you should have y= -2x + 1
3. then on the second equation subtract 4x from 4x + 2y = 2
4. now you should have 2y = -4x + 2
5. divide everything by 2
6. now you should have y = -2x + 1
7. since you got an exact answer on both of them then it is exactly one
Given the following sequence {a^k} beginning with a0=4
4,11,18,25,32,39
What is the value of a4?
Answers
==================================
Explanation:
Simply pair each value given in the sequence with a0,a1,a2,etc like so
a0 = 4
a1 = 11
a2 = 18
a3 = 25
a4 = 32
a5 = 39
Georgia's baby brother weighed less than 11 pounds when he was born. Which of the following could be the number of ounces Georgia's baby brother weighed? Select two that apply.
A
156 ounces
B
170 ounces
C
186 ounces
D
190 ounces
Answers
Answer:
Step-by-step explanation:
B :because 11 pound in Ounces is 176
If 2a = 80 and b = c, what is the measure of b
A.) 40
B.) 50
C.) 80
D.) 100
Answers
Answer:
From what I can tell from the image, b is equivalent to B.) 50°
Step-by-step explanation:
So to start off 2a=80° there is 2 a's. so you subtract 80° from 180° to get 100°.
now b=c and their is 100° left over. So 100°/2 is 50° because if b=50° and c=50° both angles equal 100°.
Answer : The correct option is, (B) 50
Step-by-step explanation:
As we are given :
2a = 80
b = c
As we know that:
The sum of interior angles of a triangle is equal to [tex]180^o[/tex].
That means,
[tex]\angle A+\angle B+\angle C=180^o[/tex]
[tex]80^o+\angle B+\angle C=180^o[/tex]
and, [tex]\angle B=\angle C[/tex]
So,
[tex]80^o+2\angle B=180^o[/tex]
[tex]2\angle B=180^o-80^o[/tex]
[tex]2\angle B=100^o[/tex]
[tex]\angle B=\frac{100^o}{2}[/tex]
[tex]\angle B=50^o[/tex]
Thus, the value of 'b' is [tex]50[/tex]
A positive number is multiplied by itself and then 7 is added. The answer is 16. What is the number?
Answers
Answer:
3
Step-by-step explanation:
To solve this you have to work backwards with what you are given.
16-7=9
Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3
3*3=9+7=16
Answer:
3
Step-by-step explanation:
Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.
16-7=9 √(9)=3
Check this by going through the same steps listed in the question:
A positive number is multiplied by itself. then 7 is added. the answer is 16
3×3=9
9+7=16
Determine whether the following statements are true or false. If false, explain why.
1) Point (3,2) to (3,-2) is a reflection over the y-axis.
2) A(1,3) to A'(-1,3) is a reflection over the y-axis
Answers
Answer:
see the explanation
Step-by-step explanation:
we know that
The rule of the reflection of a point across the y-axis is equal to
(x,y) -----> (-x,y)
The rule of the reflection of a point across the x-axis is equal to
(x,y) -----> (x,-y)
so
Verify each statement
1) Point (3,2) to (3,-2) is a reflection over the y-axis.
The statement is false
Because, is a reflection over the x-axis
A reflection over the y-axis will be
(3,2) -----> (-3,2)
2) A(1,3) to A'(-1,3) is a reflection over the y-axis
The statement is true
csc^2x – 5 csc x = 0
Answers
The solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]
To find the solutions for [tex]\( \csc^2x - 5\csc x = 0 \)[/tex], we can factor the expression:
[tex]\[ \csc x (\csc x - 5) = 0 \][/tex]
This equation is satisfied when either [tex]\(\csc x = 0\) or \(\csc x - 5 = 0\)[/tex].
1. For [tex]\(\csc x = 0\)[/tex], we know that [tex]\(\csc x\)[/tex] is the reciprocal of the sine function, and sine is 0 at multiples of [tex]\(\pi\)[/tex]. Therefore, [tex]\(x = n\pi\)[/tex] where n is an integer.
2. For [tex]\(\csc x - 5 = 0\)[/tex], solving for [tex]\(\csc x\)[/tex] gives [tex]\(\csc x = 5\)[/tex], and the sine of an angle is the reciprocal of its cosecant. Therefore, [tex]\(x = \sin^{-1}(1/5)\).[/tex]
In summary, the solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]
The complete question is probably:
What are the solutions for \( \csc^2x - 5\csc x = 0 \)?
In recent year 34% of all college students were enrolled part time if 6.1 million college students were enrolled part time that year what was the total number of college students
Answers
The total number of college students was 17.94 million.
Step-by-step explanation:
Percentage of part time students = 34%
Number of part time students = 6.1 million
Let,
x be the total number of students
According to statement,
34% of x = 6.1 million
[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]
Dividing both sides by 0.34
[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]
The total number of college students was 17.94 million.
Keywords: percentage, division
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What is the first step to take when solving this linear system of equations by the addition-subtraction method? 2x + 4y = 3 x + 3y =13 A) solve for y in terms of x B) solve for x in terms of y C) multiply the first equation by −2 D) multiply the second equation by −2
Answers
The right answer is Option D.
Step-by-step explanation:
Given equations are;
2x+4y=3 Eqn 1
x+3y=13 Eqn 2
When we use subtraction-addition method, we make one of the variables same with opposite signs so that only one variable remains after addition or subtraction.
In the given problem, we will multiply Eqn 2 with "-2" so that the x variables become equal and then we can add both the equations and solve for y.
Therefore,
The first step will be to multiply the second equation by -2 to solve the linear system of equations.
The right answer is Option D.
Keywords: linear equations, subtraction
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Answer:
It's D.
Step-by-step explanation:
It was correct on my unit test review.
What is the y-intercept of y = 5?
Answers
Answer:
Y- intercept is 5!
need some help with this please
Answers
Answer:
40 and 50
Step-by-step explanation:
We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:
x*y = 10
(x+10)*z = 25
y+z = 0.75
I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so
[tex]\frac{x miles}{hours} * \frac{yhours}{1} = xmiles*y[/tex]
I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.
We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get
(10/y+10)*z=25
Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that
y+25/(10/y+10) = 0.75
Multiplying both sides by 10/y+10 to get rid of the denominator, we get
10+10y+25=7.5/y+7.5
Then we multiply by y to get rid of the denominator
10y+10y²+25y=7.5+7.5y
Subtracting 7.5+7.5y to get everything on one side for a quadratic equation
10y²+27.5y-7.5=0
Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25
Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds
the slope is 35. The y-intercept is 550. what can you conclude?
Answers
If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
For the values you've given:
- The slope (m) is 35.
- The y-intercept (b) is 550.
From these pieces of information, you can conclude:
1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.
2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.
With these conclusions, you can write the equation of the line in slope-intercept form:
\[ y = 35x + 550 \]
This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.
Solve the equation.
a² = 100
Enter the correct answer in the boxes.
a = 10 or a = ?
Answers
When you square a number, you're essentially multiplying it by itself.
Recall that multiplying two negative numbers will result in a positive numbers. Knowing this, we know that -10 times -10 equals 100.
plzzz help !!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Y = - 2
Step-by-step explanation:
Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y
The ____ value of a digit is based on its location.
Answers
Answer:
place
Step-by-step explanation:
Answer:
The answer is " Place value"
Step-by-step explanation:
The place value determines the value of the digit in a number, based on its position.
A standard form number is divided into groups of three digits using commad. Each of these groups is called a period.
find the slope between the points (-4,5) and (-8,-5)
Answers
Answer:
[tex] \frac{5}{2} \\ [/tex]
Step-by-step explanation:
[tex] \frac{ - 5 - 5}{ - 8 - - 4} [/tex]
Y - Y divided by X - X, the Y is 5 and the X is 2 (Rise over Run)
Answer:
[tex]\displaystyle 2\frac{1}{2} = m[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 5}{4 - 8} = \frac{-10}{-4} = 2\frac{1}{2}[/tex]
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Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length of side DE is 6 cm. If the area of ABC is 5 square centimeters, what is the area of DEF ?
Answers
Answer:
Area of ΔDEF is [tex]45\ cm^2[/tex].
Step-by-step explanation:
Given;
ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Length of AB = [tex]2\ cm[/tex] and
Length of DE = [tex]6\ cm[/tex]
Area of ΔABC = [tex]5\ cm^2[/tex]
Solution,
Since, ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Therefore,
[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]
Where triangle 1 and triangle 2 is ΔABC and ΔDEF respectively.
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]
Thus the area of ΔDEF is [tex]45\ cm^2[/tex].
Find three solution of equation - 4X+2Y-5=0
(x,y) =
(x,y) =
(x,y) =
Answers
Answer:
(0,2.5), (-1.25,0) and (3,8.5)
Step-by-step explanation:
we have
[tex]-4x+2y-5=0[/tex]
This is a linear equation (equation of a line)
If a ordered pair is a solution of the linear equation, the the ordered pair must satisfy the linear equation
1) Find the y-intercept
The y-intercept is the value of the y when the value of x is equal to zero
For x=0
substitute the value of x in the linear equation and solve for y
[tex]-4(0)+2y-5=0[/tex]
[tex]2y=5[/tex]
[tex]y=2.5[/tex]
The ordered pair is (0,2.5)
2) Find the x-intercept
The x-intercept is the value of the x when the value of y is equal to zero
For y=0
substitute the value of y in the linear equation and solve for x
[tex]-4x+2(0)-5=0[/tex]
[tex]-4x=5[/tex]
[tex]x=-1.25[/tex]
The ordered pair is (-1.25,0)
3) Assume any value of x or y and solve for the other variable
For x=3
[tex]-4(3)+2y-5=0[/tex]
[tex]-12+2y-5=0[/tex]
[tex]2y=17[/tex]
[tex]y=8.5[/tex]
The ordered pair is (3,8.5)
What is the y-intercept of the function f(x) = –negative StartFraction 2 Over 9 EndFraction.x + ?
Answers
The y-intercept is 1/3
Explanation:I'll assume the function is the following:
[tex]f(x)=-\frac{2}{9}x+\frac{1}{3}[/tex]
As you can see, this is the equation of a line written in Slope-intercept form. The general rule of writing lines in this form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, which is the point at which [tex]x=0[/tex]. By comparing our function with the written rule, we can say that the y-intercept is:
[tex]\boxed{b=\frac{1}{3}}[/tex]
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Answer:
[tex]b=\frac{1}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-\frac{2}{9}x +\frac{1}{3}[/tex]
This given function is a linear function, because its variables have one as exponent, we can also say that its variables are linear.
This function, as a linear one, it's represented as a line.
Additionally, the form of this function is called slope-intercept form as
[tex]f(x)=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
So, in this case
[tex]m=-\frac{2}{9}[/tex] and [tex]b=\frac{1}{3}[/tex]
Therefore, the y-intercept of the given function is
[tex]b=\frac{1}{3}[/tex]
3. In order to enter the state fair, there is
an admission cost. Each game is $3.
Steven went to the state fair, played
4 games and spent a total of $20 on
admission and games. Assume the
relationship is linear. Find and interpret
the rate of change and the initial value.
Answers
Answer:
C = 8 + 3x
The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.
The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.
Step-by-step explanation:
Let the admission cost of the fair is $x and each game is $3.
Now, Steven went to the state fair, played 4 games and spent a total of $20 on admission and games.
So, we can write 20 = x + 4 × 3 {As the relation is linear}
⇒ x = $8
Therefore, the admission cost in the fair is $8.
Therefore, the equation that models the situation is
C = 8 + 3x ............ (1)
Where C is the total cost and x is the number of games played.
So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.
Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)
By what number should -15 raise to -1 be divided so that the quotient may be equalto -15 raise to -1
Answers
Answer:
[tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex]
Step-by-step explanation:
Given:
Dividend = [tex](-15)^{-1}[/tex]
Quotient = [tex](-15)^{-1}[/tex]
We notice that the dividend and the quotient are equal. This means the divisor is 1.
By identity property of 1, any number divided by 1 is equal to the same number or the quotient of a number divided by 1 is equal to the number itself.
So, we can write this as:
[tex]\frac{(-15)^{-1}}{1}=(-15)^{-1}[/tex]
Thus [tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex] (Answer)
Enter an equation in point-slope form for the line.
Slope is O and (6, 7) is on the line.
Answers
Answer:
[tex]\displaystyle y = 7[/tex]
Step-by-step explanation:
Since the rate of change [slope] is zero, that automatically makes our equation set equal to the y-coordinate of the ordered pair, which in this case is the y-intercept.
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Assume that µ = 500 and s = 100. Your study shows a sample of size 22 with a mean of 530 and standard deviation of 113. a. What is the most powerful test to use to test the hypothesis that the mean of the sample was drawn from the above Null Hypothesis Population? b. What is the value of the test statistic? c. What do you conclude using a = 0.052 tail?
Answers
Answer: using t - test value is 1.37<2.08( At 0.05 level of significance)
The mean of the sample was drawn from the population.
Step-by-step explanation:
Here sample size n=22
Given sample mean =530
Given population mean =500
[tex]t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }[/tex]
given sample standard deviation s=100
a) null hypothesis:- The mean of the sample was drawn from the population µ =500
Alternative hypothesis:-
The most powerful test you can use is t - distribution.
The test statistic is
[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }
here S is the standard deviation of the sample
b) The value of the test statistic
[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }
substitute given values sample size n=22
sample mean =530
sample standard deviation s =100
mean of the population µ =500
the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }[/tex]
the calculated value=1.3748
c) The degrees of freedom =n-1 = 22-1 = 21
The table value of t are 0.05 level of significance with 21 degrees of freedom is 2.08
The calculated value 1.37<2.08
∴ we accept null hypothesis at 0.05 level of significance
conclusion:-
The mean of the sample was drawn from the population.
A t-test is the most powerful test for this hypothesis. The test statistic value is calculated using t = (X - µ) / (s / √n). Based on a significance level of 0.05, we can conclude by comparing the calculated t-value with the critical t-value from t-distribution table.
Explanation:The subjects of this question are hypothesis testing and statistics.
To answer your question: a) The most powerful test to use to test your hypothesis is the t-test for single mean. This is because you have one sample mean, one hypothesized population mean, and the population standard deviation is not known.
b) The value of the test statistic can be calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in your values, the formula becomes t = (530 - 500) / (113/ √22).
c) With a = 0.05, we conclude by comparing the calculated t-value with t-distribution table (df = 22-1 = 21). If the calculated t-value exceeds the critical t-value from the t-distribution table, we reject the null hypothesis.
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A class of 32 consists of students who either have red or yellow shirts if there are 12 more people with red shirts in there are people with yellow shirt many students have red shirt
Answers
Answer:
22 people with red shirts and 10 people with yellow shirts
a punch recipe calls for equal amounts of orange and pineapple juice. pineapple juice comes in 6 ounce cans and orange juice comes in 10 ounce cans what is the least amount of each kindof juice that can be mixed with out having any left over?
Answers
Answer:
0.6 ounces
Step-by-step explanation:
A beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40% By how much does the price go up.
Answers
Answer:
It goes up my $1.80
Step-by-step explanation:
You multiply $4.50 by 0.40 and you get 1.80 and that’s how much it goes up by
A recipe for 12 servings of soup calls for 8 cups of chicken broth. How
many cups of broth are needed to make 30 servings of the soup?
Answers
Answer:
20 cups of broth are needed to make 30 servings of the soup.
Step-by-step explanation:
This is a typical proportion math problem.
Just set up the proportion and solve for the unknown variable, let it be x, because it's simple to use.
12/8=30/x
simplify 12/8 to 3/2,
3/2=30/x
cross product,
2*30=3*x
60=3x
x=60/3
x=20
Number of cups of broth needed for making 30 servings is 20.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
We have,
Cups of broth needed for 12 servings of soup = 8 cups
Let cups of broth needed for 30 servings of soup = x cups
Using the concept of proportion,
12 / 8 = 30 / x
Doing the cross multiplication,
12x = 8 × 30
12x = 240
x = 240 / 12
x = 20
Hence 20 cups of broth are needed to make 30 servings of the soup.
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what is the simplified expression to 3.4m+2.4m
Answers
Final answer:
The simplified expression for 3.4m + 2.4m is 5.8m. You simply add the coefficients of like terms.
Explanation:
To simplify the expression 3.4m + 2.4m, we need to combine like terms. The term 'like terms' refers to terms that have the exact same variable raised to the same power. In this case, both terms have 'm' as the variable, and it's not raised to any power (which is the same as being raised to the power of 1).
Combine the coefficients (numerical parts) of the like terms:
3.4m + 2.4m = (3.4 + 2.4)m
Add the coefficients: 3.4 + 2.4 = 5.8
Therefore, 3.4m + 2.4m = 5.8m.
Find percent increase, round to the nearest percent
From 24 teachers to 225 pencils
Answers
Answer: 838% to the nearest percent
Step-by-step explanation:
225 - 24 =201
=201/24 * 100
= 838% to the nearest percent