Answer:
Step-by-step explanation:
The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function
The function given is \(F(x, y)=\frac{1}{\sqrt{x^2-y} }\) , the denominator cannot be 0.
So we set up the equation
\(\sqrt{x^2-y} \neq 0\)
\(\sqrt{x^2-y}^{2} \neq 0x^2-y\neq 0x^2\neq y\)
And that the the square root needs to be more than 0.
\(\sqrt{x^2-y}\geq 0\)
\(x^2-y\geq 0\)
\(x^2\geq y\)
So we can conclude that all values of \(x^{2}\) must be greater y
That means that our domain is all X values greater than\(\sqrt{y}\)
jean rents an electric sander for $2.50 per hour plus $6.00 for the sand paper. what is the cost of renting the sander for 10 hours ? use the function c = 2.5h + 6
Its a hard question i really don't know
Sarah is spending the day at a state fair. While at the fair, she can play games or ride rides. When Sarah arrives at the fair, she purchases 15 tickets and wants to use all of the tickets that she purchases. Playing a game at the fair requires three tickets, and riding a ride at the fair requires six tickets. To make her trip to the fair worthwhile, Sarah decides she must participate in seven activities at the fair.
Sarah requires the purchase of additional 12 tickets to ensure her participation in the seven activities at the fair.
How are the additional (missing) tickets determined?The additional tickets required by Sarah can be determined as follows:
Number of tickets purchased initially = 15
Number of tickets for playing a game = 3
Number of tickets for riding a ride = 6
Sarah can play five (5) games with 15 tickets (15/3).
Sarah can then purchase 12 additional tickets (6 x 2).
The later action enables Sarah to participate in 5 games and 2 rides, making it a total of 7 activities.
Thus, by purchasing additional 12 tickets, Sarah can participate in 5 games and 2 rides, making it a total of 7 activities.
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Question Completion:How many more tickets does Sarah require to ensure her participation in the seven activities at the fair?
How much must be deposited today into an account in order to save $70000in 8 years with annual compounding and an apr of 7%
Answer:
See below
Step-by-step explanation:
FV = pv ( 1 + i)^n i = decimal interest per period (year) = .07
n = periods = 8
FV = future value = 70 000
pv = present value = the maount to deposit
70 000 = pv ( 1 + .07)^8 pv = $ 40740.64
Identify the type of function below.
F(x) = 4x + 2
Answer: I cheated and looked it up. It says parabola or basic parabola.
find the mean of the following numbers 7,21,2,17,3,13,7,4,9
Answer:
9.222222222
Step-by-step explanation:
7+21+2+17+3+13+7+4+9 = 83
7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222
_____________________________
Hey!!
Solution,
Given data=7,21,2,17,3,13,7,4,9
summation FX= 83
N(total no. of items)=9
Now,
Mean=summation FX/N
= 83/9
=9.23
So the answer is 9.23
__________________________
An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?
Answer:
16 in.
Step-by-step explanation:
We have the ratio
How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of
Now we need to know how many inches there would be if the number of feet is 24:
Cross multiply to get
3x = 48 so
x = 16 in.
The length of the line on the blueprint of the wall will be 18 inches.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.
Then the scale factor of the blueprint will be
Scale factor = 3/4 inches per foot
If the east wall of the building is 24 feet long.
Then the length of the line on the blueprint of the wall will be
Length = 24 feet x scale factor
Length = 24 x (3/4)
Length = 6 x 3
Length = 18 inches
Thus, the length of the line on the blueprint of the wall will be 18 inches.
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Hello, I need help with this problem.Quick answer is OK
We are given the set {-2,-1,0,1,2} and the definition of piecewise function as follows
\(f(x)=\begin{cases}{-3\text{ if x<0}} \\ {-1\text{ if x=0}} \\ {x\text{ if x>0}}\end{cases}\)We only need to calculate the values of the function over the given set and then plot them. Note that as -2 and -1 are less than 0, if we want to calculate the value of f for these values, we should apply the first row of the definition of f. So we have that
\(\begin{gathered} f(\text{ -2\rparen= -3} \\ f(\text{ -1\rparen= -3} \end{gathered}\)when x=0 we are given the explicit value of the function. That is
\(f(0)=\text{ -1}\)Note that as 1 and 2 are greater than 0, we use the last row of the definition of f. That is, we output the same value as input. So we have
\(\begin{gathered} f(1)=1 \\ f(2)=2 \end{gathered}\)we collect this information on a table. So we get
x f(x)
-2 -3
-1 -3
0 -1
1 1
2 2
This can be summarized on the pair points (-2,-3), (-1,-3), (0,-1), (1,1) , (1,2).
If we plot this on a graph, we get
which corresponds to option C
A 10-sided fair die, a 20-sided fair die, and a 6-sided fair die are rolled. What is the probability of all three happening:
Showing 8 on the first die
Showing 21 on the second die
Showing an odd number on the third die
Probability =
(Enter your answer as a reduced fraction.)
three fair dies are rolled. The first die is a 10-sided fair die and it shows 8.The second die is a 20-sided fair die and it shows 21.The third die is a 6-sided fair die and it shows an odd number. the probability is 1/400.
The probability that all three are occurring is given by the probability of the first die multiplied by the probability of the second die multiplied by the probability of the third die
Probability = P(first die shows 8) * P(second die shows 21) * P(third die shows an odd number)
The probability of the first die showing 8 is 1/10The probability of the second die showing 21 is 1/20The probability of the third die showing an odd number is 3/6 (as there are 3 odd numbers out of 6 numbers)Therefore, the probability of all three happening is:
Probability = P(first die shows 8) * P(second die shows 21) * P(third die shows an odd number) = (1/10) * (1/20) * (3/6) = 1/400
Thus, the probability is 1/400.
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The perimeter of the TCL 3-Series Roku Smart TV is 112 inches. The width of the TV is 16 inches greater than its height. Find the width and the height of the TV.
Answer: Height = 20 inches, Width = 36 inches
Step-by-step explanation:
Let the height be \(h\) and the width be \(h+16\).
Using the formula for the perimeter of a triangle,
\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)
What is -20/2(7 2/3)
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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100 points!!! Algebra graphing question. Describe the end behavior of the graph in each function. Photo attached. Thank you!
Answer: your originally supposed to use arrows to show end behaviors
graph one down /up
graph two down/ down
graph three up/ down
Step-by-step explanation:
pretty sure this is the answer if your asking for the end behaviors
Slope 3/5 yintercept2 write an equation slope-intercept form
The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.
To write the equation of a line in slope-intercept form, we use the formula:y = mx + b
where:
- y represents the dependent variable (the vertical axis)
- x represents the independent variable (the horizontal axis)
- m represents the slope of the line
- b represents the y-intercept, the point where the line intersects the y-axis.
In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:
y = (3/5)x + 2
This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).
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Which of the following is a divisor of 12! · 6! + 12! + 6! + 1?
A. 21
B. 77
C. 91
D. 115
E. 143
Hint : Use Wilson's Theorem\(.\)
Answer:
C. 91Step-by-step explanation:
Rewriting the given as factors:
12! · 6! + 12! + 6! + 1 =12!(6! + 1) + (6! + 1) =(12! + 1)(6! + 1) =((13 - 1)! + 1)((7 - 1)! + 1)As per Wilson's theorem, if n is prime number, (n - 1)! + 1 is divisible by n
As per above, 13 and 7 are both prime numbers, so the expression is divisible by both 7 and 13:
7*13 = 91So correct choice is C
What is the smallest positive integer which when divided by 5 leaves a remainder of 3?
The smallest positive integer which when divided by 5 leaves a remainder of 3 is 8
How to determine the smallest positive integerFrom the question, we have the following parameters that can be used in our computation:
Divisor = 5
Remainder = 3
Using the above as a guide, we have the following:
Smallest integer = Divisor + Remainder
So, we have
Smallest integer = 5 + 3
Evaluate
Smallest integer = 8
Hence, the smallest is 8
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I need to know this answer
The equation of the line is y = (3/2)x - 1/2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).
Now,
The equation of a line.
y = mx + c
The line passes through points (3, 4) and (5, 7).
m = (7 - 4) / (5 - 3)
m = 3/2
Slope = 3/2 _____(1)
Now,
(3, 4) = (x, y)
4 = 3/2 x 3 + c
4 = 9/2 + c
c = 4 - 9/2
c = (8 - 9) / 2
c = -1/2
y-intercept = -1/2 ____(2)
Now,
y = mx + c
From (1) and (2),
y = (3/2)x - 1/2
Thus,
The equation of the line is y = (3/2)x - 1/2.
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The complete question.
Find the equation of a line that [passes through the point (2, 4), and (5, 7).
Consider parallelogram QRST below. Use the information given in the figure to find m
The missing values are
<UTQ = 41 degree
x= 1
<UQT = 47 degree
We have a parallelogram QRST.
We know that the opposite sides of the parallelogram is equal and parallel then
QR || ST
QT || SR
Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)
<UTQ = 41
Similarly, <UQT = <SRQ = 47
Now, RU = UT
2x + 1= 3
2x = 2
x= 1
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y
4
Solve for y.
Then, find the side lengths of the
largest triangle.
Fill in the green blank.
8
X
2
+
2
8
y
y
[?]
X
Enter
Help
Skip
Answer:
y = 4\(\sqrt{5}\) , ? = 10
Step-by-step explanation:
using Pythagoras' identity on the smallest right triangle
x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )
x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)
using Pythagoras' identity on the middle right triangle
y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )
y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)
using Pythagoras' identity on the largest right triangle
?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100
Take square root of both sides
? = \(\sqrt{100}\) = 10
One number is 5
more than another. The difference between their squares is 75
. What are the numbers
Answer:
The numbers are 5 and 10.
Step-by-step explanation:
Let x be one of the numbers. We know the other number is 5 more, so that number can be x+5.
We can square the bigger number lile this:
(x + 5)^2
Also we can squared the smaller number, x^2.
They said the difference was 75. Difference means subtracting.
(x+5)^2 - x^2 = 75
square the terms
x^2+10x+25-x^2=75
combine like terms.
10x + 25 = 75
subtract 25
10x = 50
divide by 10
x = 5
So the smaller number is 5 and the larger number
x + 5
= 5 + 5
= 10
The numbers are 5 and 10.
One number is 5 more than the other.
The difference if their squares 10^2 and 5^2 is
10^2 - 5^2
= 100 - 25
= 75
The difference is 75.
prove that for every positive rational number r satisfying the condition r2<2 one can always find a larger rational number r h (h>0 ) for which (r h)2<2 .
Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.
Consider the number rh = r + h. We have:
(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16
= r^2 + 2 + (2 - r^2)/16
< 2 + 2 + (2 - 2)/16 = 2.
Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.
Step-by-step explanation:
pls do the assignment for me I will give brainiest just upload and do the work for me
Answer:
lazyyyy
Step-by-step explanation:
Solve the equation 2/3x - 1/5x = x - 1
Answer:
To solve the equation:
2/3x - 1/5x = x - 1
First, we need to find a common denominator for 2/3 and 1/5, which is 15. So we can rewrite the equation as:
(10/15)x - (3/15)x = 15/15 x - 1
Simplifying the left side:
(7/15)x = 15/15 x - 1
Multiplying both sides by 15:
7x = 15x - 15
Subtracting 7x from both sides:
-8x = -15
Dividing both sides by -8:
x = 15/8 or 1.875
Therefore, the solution to the equation is x = 1.875.
Please help 9th grade math question
The quadratic function f(x) =\(3(x+3)^2 - 7\) has a minimum at x = -1, and the minimum value is 5.
To determine whether the quadratic function f(x) =\(3(x+3)^2 - 7\)has a minimum or maximum, we can examine the coefficient of the x^2 term, which is positive (3 in this case).
When the coefficient of the x^2 term is positive, the parabola opens upward, indicating that the function has a minimum value. The vertex of the parabola represents the minimum point.
Now let's find the coordinates of the vertex, which will give us the minimum value of the function.
The general form of a quadratic function is f(x) =\(ax^2 + bx + c\), where the vertex can be found using the formula:
x = -b / (2a)
In our case, a = 3 and b = 3*2 = 6 (from (x+3)^2).
Substituting the values into the formula, we have:
x = -6 / (2 * 3)
x = -6 / 6
x = -1
To find the y-coordinate of the vertex, we substitute the x-value (-1) into the function:
\(f(-1) = 3((-1)+3)^2 - 7\)
\(f(-1) = 3(2)^2 - 7\)
f(-1) = 3(4) - 7
f(-1) = 12 - 7
f(-1) = 5
The graph of this function will have a downward-opening parabola, and the vertex will be the lowest point on the curve.
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Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=' for if necessary.
-2(5x + 1) > 48
Answer:
x < -5
Step-by-step explanation:
-2(5x+1) >48
-10x-2 > 48
-10x-2+2 > 48+2
-10x > 50
p.s : when dividing by a negative number with inequalities, change the sign, i.e. < would then be >....
therefore:
x < -5
A grocery store has 10 cartons of yogurt for sale, of which 4 are raspberry. What is the probability that a randomly selected carton of yogurt will be raspberry? Write your answer as a fraction or whole number.
Answer:
2/5
Step-by-step explanation:
4 raspberry / 10 total
4/10
2/5
Write the standard form of the equation of the circle with radius 8 and center (10,−7).
The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
What is the standard form of the equation of a circle?The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.
We have given that circle having radius of 8 units. Thus, r = 8.
Since we know that circle having the center (10,−7).
Thus, the equation of the circle, with a radius of 8 units is;
(x - h)² + (y - k)² = r²
(x - 10)² + (y + 7)² = 8²
Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
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Three numbers sum to 117. The second number is 10 less than the first. The third number is 2 more than half the first. What are the three numbers?
Answer:
Step-by-step explanation:
The three numbers are 50, 40, and 27.
We can solve this equation by setting up a system of equations.
Let x be the first number, y be the second number, and z be the third number.
x + y + z = 117
y = x - 10
z = (1/2)x + 2
Substituting the equation for y into the first equation, we get:
x + (x - 10) + (1/2)x + 2 = 117
2x - 8 = 117
2x = 125
x = 62.5
Substituting this value of x into the other equations, we get:
y = x - 10 = 62.5 - 10 = 52
z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5
Rounding these values, the three numbers are 50, 40, and 27.
PLS HELP ! ILL MARK BRAINLIST
Answer:
I am pretty sure your answer is right
Step-by-step explanation:
Simplify the following expression: (4x2)2 • (3x3)3
Answer:
432x^13
Step-by-step explanation:
(4x^2)^2 • (3x^3)^3
We know that a^b^c = a^(b*c)
4^2 x^2^2 * 3^3 x^3^3
16 x^4 * 27 x^9
We know that a^b ^ a^c = a^(b+c)
16*27 x^(4+9)
432x^13
Answer:
432x¹³
Step-by-step explanation:
( 4x² ) ² • ( 3x³ ) ²
( 16x²)² • ( 27x³)²
\(16 x{}^{2 \times 2} \times 6 {}^{3 \times 3 } \\ 16x {}^{4} \times27 {}^{9} \)
\((16 \times 27)x {}^{4 + 9} \)
432x¹³
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Which number(s) have a 5 that is 10 times the value of the 13,725 in ?
Answer:
I will give you three, but the answer is the number that has a 50
Step-by-step explanation:
52
654
7657
50 is the numbers that have a 5 in 10 times the value of the 13,725.
What is place value?Place value is the value of each digit in a number.
For example, the 5 in 350 represents 5 tens, or 50; however the 5 in 5006 represents 5 thousands, or 5000.
Now the given number is,
13,725
10 times of the number is givens as,
13,725*10
or, 137,250
here place value of 5 in 137,250 is 5 tens or 50.
Therefore, 50 is the numbers that have a 5 in 10 times the value of the 13,725.
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