The domain of the function is 1 ≤ x < 2.
What is domain ?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).
We have f : [tex]\frac{1}{\sqrt{x-1} } + \frac{1}{\sqrt{2-x} }[/tex]
[tex]\sqrt{x-1}[/tex] ≥ 0
x- 1 ≥ 0
x ≥ 1
Similarly , [tex]\sqrt{2-x}[/tex] > 0
2 - x > 0
2 > x
So our domain is 1 ≤ x < 2.
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Angelina’s family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
The ordered pair (–2, 7) is viable.
The ordered pair (0, 7) is viable.
The ordered pair (17, 3) is viable.
The ordered pair (20, 5) is non-viable.
The conclusion which is correct among the answer choices as given in the task content is; The ordered pair (17, 3) is viable.
Which conclusion among the answers choices is correct?It follows from the task content that the conclusion which is valid be identified among the answer choices.
Since it is given that; there is a relationship between the number of visit and hole-in-one winners.
The statement above indicates that the number of visitors must be greater than the number of winners. This follows from the fact that there is no winner if there are no visitors.
Hence, since x is the number of visitors and y is the number of winners, the ordered pair which is viable is; (17, 3).
The ordered pair (20, 5) is viable too. However, the last answer choice indicates that it id not and hence, is incorrect.
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Answer:
(17,3)
Step-by-step explanation:
I got it on FLVS
answer this solve 2k+6k=h for k
The value of the variable k in the equation given as 2k + 6k = h is k = h/8
How to determine the solution for k?From the question, the equation is given as
2k + 6k = h
Evaluate the like terms
i.e. We add 2k and 6k together.
This gives 8k
So, we have the following equation
8k = h
Divide both sides of the equation by 87
So, we have the following equation
8k/8 = h/8
Evaluate the quotient in the equation
k = h/8
The equation cannot be further simplified
Hence, the solution for k is k = h/8
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ASAP!!! A bike trail starts at (4.2,−30.5) and ends at (4.2,9.7) on a map. Each unit represents 1 kilometer. What is the distance from start of the trail to the end?
Explanation:
The x coordinates are the same, so we subtract the y coordinates and use absolute value to ensure the result isn't negative.
|-30.5 - 9.7| = |-40.2| = 40.2
One unit represents 1 km, so 40.2 units represent 40.2 km
This converts to 40,200 meters. Multiply by 1000 to go from km to meters.
Engl Write the linear equation that gives the rule
for this table.
Hon
Sch
Dire
Sch
Cale
Con
Car
Sup
X
0
1
2
3
y
23
24
25
26
Write your answer as an equation with y first,
followed by an equals sign.
y=x+23 is the linear equation that gives the rule for the given table .
Explanation of the concept of linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
The following is how the linear equation can be expressed in a slope-intercept form:
y = mx + b
where
slope = m
y-intercept = b
Using the table we get two points:
(1,24) and (2,25)
slope= y2-y1/x2-x1
= 25-24/2-1
=1
Now we have to calculate B using the point (1,24) and putting values in equation y=mx+b
24=1+b
b=23
So the equation is :
y=x+23
Therefore the linear equation for the given set of data table is y=x+23.
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Given f(x)=2x^3+kx-11 and x-1 is the factor of f(x), then what is the value of k?
The value of k in the expression is equal to 9.
The expression is in the form of Cubic polynomial. A cubic polynomial is the one which can be written in the form y = ax³ + bx² + cx + d where a, b, c and d are coefficients and x, and y are independent and dependent variables respectively. The cubic polynomial f(x) = 2x³ + (k)x - 11 has a factor equal to (x-1). If it is the factor, then x = 1 is the solution of cubic polynomial and at x = 1 the value of f(x) = 0.
2(1)³ + k(1) - 11 = 0
2 + k - 11 = 0
k - 9 = 0
=> k = 9 which is the required value.
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help please with this question
Gagu will be paid £1248 per month after the increase.
Given,
The amount Gagu is paid = £1200 per month
The increase he is going to get = 4%
We have to find the amount Gagu gets after the increase:
First we have to find the increment amount:
That is,
4% of 1200
= 1200 × (4/100)
= 12 × 4
= 48
Here,
£48 is the increment amount Gagu will get.
Now we can calculate the monthly amount gagu will be paid after the increase.
That is,
1200 + 48 = 1248.
Therefore,
Gagu will be paid £1248 per month after the increase.
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Michael is driving to Hollywood, California. Hollywood is 1,375 miles from Michael's. home. If Michael spends 4 days driving to Hollywood, what is the fewest number of miles he can drive each day?
Answer:
343.75
Step-by-step explanation:
dividing the number of miles by the number days to get fewest equal number miles per each day
Please write the answer on the picture so i understand carefully^^need rn
Required:
We need to fill the given diagram with suitable words.
Explanation:
Consider the first line.
There is a choice of fish-bottled water is coming from fish and bottled water.
Consider the second like there is Chicken-bottled water and we have bottled water.
There must be chicken under food.
There are only three types of drink that are Bottled water, Soft drink, and juice.
In drinks for fish, there are already two drinks Bottled water and juice so the remaining is Soft drinks.
Chicken and juice give a choice of Chicken-Juice.
Vegetable and Juice give a choice of Vegetable- Juice.
need help with exam study sheet
The rate of change is (-1)
To solve this, we need to look at graphic to know the values of the function f(x) when x is equal to 1 and 3.
Then we have two points of the graph: (1,6) and (3,4).
The rate of change between two points is:
[tex]m=\frac{\text{change in f(x)}}{change\text{ in x}}[/tex]In this case,
[tex]m=\frac{4-6}{3-1}=\frac{-2}{2}=-1[/tex]Note that its the same whatever coordinate put first:
[tex]\frac{6-4}{1-3}=\frac{4-6}{3-1}=-1[/tex]But when you do the difference between the coordinates, make sure to respect the order: if you use the y coordinate of the point P minus the y coordinate of point Q, you must to do the same for the x coodinate; Px-Qx
What is the equation of the line perpendicularto y = 1/2x + 6 that passes through the point(4, 1)?
Two lines are perpendicular when their slopes are opposite.
You have the equation;
[tex]y=\frac{1}{2}x+6[/tex]You can identify the slope as the number next to the x (y=mx+b, m is the slope)
the slope in the given equation is 1/2
The slope of the perpendicular line will be the opposite
¿What is the constant term missing in the perfect square that begins with x ^ 2-20xx
2
−20xx, squared, minus, 20, x?
Some of the terms of an equation that has missing terms will be eliminated.
100 is the missing term that transforms (x² - 20) into a perfect square.
What is a perfect square?
A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent. For instance, the number 25, which is the product of the integer 5 multiplied by itself, is a perfect square because 5 x 5 = 25.
The missing term will be calculated in the next step.
Use k to represent the x-coefficient.
We thus have:
k = -20
Divide both sides by 2
k/2 = - 10
squaring both the sides,
(k/2)² = (- 10)²
=> (k/2)² = 100
This means that the term that is lacking is 100.
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Question:
What is the missing constant term in the perfect square that starts with x^2 -20x?
PLEASE HURRYYYY
The coordinates of midpoint M and endpoint E of a segment are M(35, –3) and E(15, 26). Students were asked to find two equations that could be used to find the coordinates of the other endpoint, F(x2, y2).
Josiah set up the equations as follows:
Which statement best describes Josiah’s work?
The −3 and 35 should be switched.
The 15 and 26 should be switched.
The equations should be
The equations are correct.
The equations for the coordinates of the endpoint F should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.
How to derive the equations for the missing endpoint of a line segment
In this problem we know the coordinates of the endpoint E and the midpoint M of the line segment EF and we need to derive expressions of the coordinates of the endpoint F by the midpoint formula:
M(x, y) = 0.5 · E(x, y) + 0.5 · F(x, y)
2 · M(x, y) = E(x, y) + F(x, y)
F(x, y) = 2 · M(x, y) - E(x, y)
If we know that M(x, y) = (35, - 3) and E(x, y) = (15, 26), then the coordinates of the endpoint F are:
F(x, y) = 2 · (35, - 3) - (15, 26)
F(x, y) = (70, - 6) + (- 15, - 26)
F(x, y) = (55, - 32)
The equations should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.
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The endpoint F's coordinates should be given by the formula
x = 2×35 - 15 and y = 2×(- 3) - 26.
What is the procedure to find the other endpoint?In order to solve this problem, we need to derive expressions for the coordinates of the endpoint F using the midpoint formula.
We know the coordinates of the endpoint E and the midpoint M of the line segment EF.
M(x, y) = 0.5×E(x, y) + 0.5×F(x, y).
2×M(x, y) = E(x, y) + F(x, y).
F(x, y) = 2×M(x, y) - E(x, y).
Given that M(x, y) = (35, -3) and E(x, y) = (15, 26), the endpoint F's coordinates are,
F(x, y) = 2×(35, - 3) - (15, 26).
F(x, y) = (70, - 6) + (- 15, - 26).
F(x, y) = (55, - 32).
The equations should be x = 2×35 - 15 and y = 2×(- 3) - 26.
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A line is drawn so that it passes through the points (-6,0) and (8,5). What is the slope of the line? Round the answer
to the tenths place. If the answer is a whole number than make the tenths place a zero to be counted as correct.
Answer:0.4
Step-by-step explanation:
just do y2-y1 over x2-x1 which gives 5/14
and convert that to a decimal which is .3571 and round it to get .4
Two brothers, Steven and Michael, each inherit $35000. Steven invests his inheritance in a savings account with an annual return of 1.8%, while Michael invests his inheritance in a CD paying 6% annually. How much more money than Steven does Michael have after 1 year?
$1470 more money does Michael have than Steven after 1 year.
What is Rate of Interest?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Rate of interest is simple interest for Steven in a savings account. He can withdraw his money any time he wishes to.
Steven will receive after 1 yr an interest payment of
=35000×1.8/100
=35000×0.018
=630
Michael invests his inheritance in a CD (Certificate of Deposit) account. He gave up access to his money for a specified period of time. Assuming that given rate of interest is annual.
=35000×6/100
=35000×0.06
=2100
Therefore, Micheal has more money than Steven.
=2100-630
=1470.
Hence $1470 more money does Michael have than Steven after 1 year.
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Ruben thinks of a whole number.
When he divides his number by 4, the result has 1 decimal place and is
greater than 6 but less than 7.
What is ruben’s original number
what 10 + 10 -2+123-85544
Answer: -85403
Step-by-step explanation:
2. Ron's car left four skid marks on the road after he slammed his foot
on the brake pedal to make an emergency stop. The police measured
them to be 55 ft, 55 ft, 62 ft, and 62 ft. What skid distance will be
used when calculating the skid speed formula?
The skid distance value that will be used when calculating the skid speed formula is 58.5 ft.
What is average of values and how is it defined?
The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. As a result, the following is the mathematic average formula:
Average = Sum of values/Set of values = (x₁ + x₂ + ... + xₙ)/n
Given, the first skid distance calculated, in feet = x₁ = 55
The second skid distance calculated, in feet = x₂ = 55
The third skid distance calculated, in feet = x₃ = 62
The fourth skid distance calculated, in feet = x₄ = 62
Therefore using the formula for average mentioned in the literature at n=4, we have,
Average skid distance = (55 + 55 + 62 + 62)/4 = 234/4 = 58.5 ft.
Thus, the skid distance value that will be used when calculating the skid speed formula is 58.5 ft.
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What is the value of n?
n–2=10n+42
Answer:
Step-by-step explanation:
n-2=10n+42
add 2 to both sides
n-2+2=10n+42+2
simplify
n=10n+44
subtract 10n from both sides
n-10n=10n+44-10-n
simplify
-9n=44
divide both sides by -9
-9n/-9=44/-9
n=-44/4
While on the trip to Galveston the boys got
hungry and sent Spencer to the store. Spencer
paid $9.03 for 2.1 pounds of flounder. What was
the price per pound Spencer paid for the
flounder?
Answer:
4.3 dollars per pound
Step-by-step explanation:
price / pound = ?
$9.03 / 2.1 lbs. = 4.3
Calculate the volume of a hemisphere.. diameter is 11cm
Pls help with all steps
The volume of the hemisphere is found as 695.55 cm³.
What is termed as the hemisphere?The term hemisphere can be broken down into hemi as well as sphere, where hemi implies half and sphere is a 3D mathematical shape. As a result, a hemisphere is a three-dimensional geometric shape that really is half of a sphere, with one side flat and the other as a circular bowl. It is created by cutting a sphere at the centre point along its diameter, resulting in two equal hemispheres. The base or face of the hemisphere is the flat face of a hemisphere.The formula for finding the volume of the hemisphere is;
V = (4/3)πr³
where, π = 3.14
r = radius
For the given question, the diameter of the hemisphere is 11 cm.
Radius = 11/2 = 5.5 cm.
Put the value in formula.
V = (4/3)×3.14×5.5³
V = 695.55
Thus, the volume of the hemisphere is found as 695.55 cm³.
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please help me I don't get this
Answer:
(10, 1) is a solution to this equation.
Answer: your answer will be (10, 1)
Step-by-step explanation:
i just watch a mathematics video
It is given that the equation (mx)²+ 5nx+4=0 has two equal real roots while the quadratic equation px²-x+m=0 has two distinct roots where m,n and p are constants. Express the range of n in terms of p
Given:
[tex](mx)^2+5nx+4=0\text{ has two equal real roots}[/tex][tex]px^2-x+m=0\text{ has distict roots. }[/tex]Taking the first equation:
[tex]a=m^2\text{ ; b=5n ; c=4 }[/tex][tex]b^2-4ac=0[/tex][tex]25n^2-4m^2(4)=0[/tex][tex](5n)^2-(4m)^2=0[/tex][tex](5n+4m)(5n-4m)=0[/tex][tex]5n+4m=0\text{ ; 5n-4m=0}[/tex][tex]m=-\frac{5}{4}n\text{ ; m=}\frac{5}{4}n[/tex][tex]4m=-5n\text{ ; 4m=5n}[/tex]Taking the second equation:
[tex]a=p\text{ ; b=-1 ; c=m}[/tex][tex]b^2-4ac>0[/tex][tex]1-4pm>0[/tex]If 4m=5n,
[tex]1-p(5n)>0[/tex][tex]1>p(5n)[/tex][tex]\frac{1}{5p}>n[/tex]If 4m=-5n,
[tex]1-p(-5n)>0[/tex][tex]1+5pn>0[/tex][tex]5pn>-1[/tex][tex]n>-\frac{1}{5p}[/tex]Range of n in terms of p:
[tex]\frac{1}{5p}>n>-\frac{1}{5p}[/tex][tex]-\frac{1}{5p}-12=-6(-8n+6) + 8(-4+n)
Answer:
n = 1
Step-by-step explanation:
-12 = -6(-8n + 6) + 8(-4 + n)
multiply our right side:
-12 = 48n - 36 -32 + 8n
combine n terms on right side:
-12 = 56n - 36 -32
combine numbers on right side:
-12 = 56n - 68
add 68 to both sides:
-12 + 68 = 56n - 68 + 68
56 = 56n
divide both sides by 56:
56/56 = 56n/56
n = 1
check:
-12 = -6(-8(1) + 6) + 8(-4 + (1))
-12 = -6(-8 + 6) + 8(-3)
-12 = -6(-2) + 8(-3)
-12 = 12 - 24
-12 = -12
Answer:
n=1
It's the answer I would tell u step by step but I can't cuase it will be kinda confusing
2. Alisha Gregory is a telephone installer. She is married and claims 2 allowances.
Her state personal exemptions total $76.92 per week. The state tax rate is 3.0% of
taxable income. Local income tax is 1.5% of gross. Medical insurance costs $1,940
a year, of which the company pays 60%.
The net pay of Alisha Gregory is $30606.4
Since we are given the weekly gross pay of her is $640
The annual gross pay will be 52 * 640 =33280.
Here the local income tax is 1.5% of the gross, which is 1.5/100 * 33280 = 499.2 and it is also specifically said that the state tax is the 3.0% of taxable income.
So we have:
3/100 * 33280= 998.4
The medical insurance is $1,940 for a year from where the company pays 60 %
For which we have:
60/100 *1940
= 1164
At the last he pays $4.50 for union dues and $7.50 for others.
Since we know that the net pay is nothing but the amount we get after subtracting the deductions from the annual gross pay
So the net pay = 33280- (499.2+998.4+1164+4.50+7.50)
= 33280 -(2673.6)
= 30606.4
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Work out the following calculations and give your answer to the nearest 10. A)23x46 b)25x68
Answer:
A) 1060 (corrected to the nearest 10) B) 1700
Step-by-step explanation:
A) the answer is 1058 which taken to the nearest 10 is 1060
B) the answer is 1700 which does not need to be corrected
whats 2+1 and 40+9 and 56+3? and 2x0 and 5 x5 equal. it'll help tyyyyyyyyyy
also what is inside a squishmallow?? and how are rulers and pens made?
Answer:
2 + 1 = 3
40 + 9 = 49
56 + 3 = 61
2 x 0 = 0
5 x 5 = 25
Step-by-step explanation:
I think Squishmallows are made of fluff and cotton.
As for rulers, WOOD
Pens, ink, and plastic
hahahaaha i cant believe no one answered this yet, they probably thought this was an actual math problem they had to use much braincells for-
The answers for addition are 3,49,59 and multiplication are 0 and 25.
What are mathematical operators?Any symbol that denotes a mathematical operation is known as an operator. Examples are d/dx and Square root of x (which implies that the square root should be taken) (which indicates differentiation with respect to x is to be performed).
What are the five mathematical operators?These operators are + for addition, - for subtraction, * for multiplication, / for division, and % for percentage (modulo).
So:
2+1=3
40+9=49
56+3=59
2*0=0
5*5=25
Therefore,The solutions to the addition and multiplication problems are 0 and 25 respectively.
For the other part
Squishmallows are made of cotton and fluff.
rulers are made of WOOD
Ink and plastic and metal is used to make pens.
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Levi and James collect baseball cards. Levi
has four times as many cards as James. If
the total number of cards they have is 600,
how many cards does each boy have? Write an equation
Step-by-step explanation:
l = number of Levi's cards
j = number of James' cards
l = 4j
l + j = 600
whey we use the first identify in the equation we get
4j + j = 600
5j = 600
j = 120
l = 4j = 4×120 = 480
Levi has 480 cards, James has 120 cards.
Alina and Cesar estimated the number of miles they drove during a trip.
Alina estimated the number of miles they drove in the morning.
Cesar estimated the number of miles they drove in the afternoon.
Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.
The statements about Alina's and Cesar’s estimates should be completed as follows:
Alina is 5 miles off the actual mileage of 50 miles. That is a percent error of 10%. Cesar is 10 miles off the actual mileage of 200 miles. That is a percent error of 5%. Because Alina's mileage is lesser than Cesar's mileage, each mile of error results in a greater percent error.What is percentage error?Percentage error is also referred to as percent error and it can be defined as a measure of the extent to which an experimental numerical value differs from the actual (theoretical) numerical value.
Mathematically, percentage error can be calculated by using this expression;
[tex]Percent\; error = \frac{Actual\;value - Experimental\;value}{Experimental\;value} \times 100[/tex]
For the Alina's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 50 miles - 45 miles
Difference = 5 miles.
Next, we would determine Alina's percentage error as follows:
Percentage error = 5/50 × 100
Percentage error = 500/50
Percentage error = 10%.
For the Cesar's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 200 miles - 190 miles
Difference = 10 miles.
Next, we would determine Cesar's percentage error as follows:
Percentage error = 10/200 × 100
Percentage error = 1000/200
Percentage error = 5%.
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Complete Question:
Alina and Cesar estimated the number of miles they drove during a trip. Alina estimated the number of miles they drove in the morning. Cesar estimated the number of miles they drove in the afternoon. Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.
Alina's Estimate Actual Mileage
45 miles 50 miles
Cesar's Estimate Actual Mileage
190 miles 200 miles
Alina is ___ miles off the actual mileage of 50 miles. That is a percent error of %.
Cesar is ___ miles off the actual mileage of 200 miles. That is a percent error of %.
Because Alina's mileage is _____ than Cesar's mileage, each mile of error results in a ____ percent error.
Given the equation Ax+By=C, solve for y.
A. y= C/B - Ax
B. y= C/Ax + B
C. y= C + Ax/B
D. y= -Ax/B + C/B
Answer: Choice D
Step-by-step explanation
First, subtract Ax from both sides:
Ax - Ax + By = C - Ax
By = C - Ax
Now, divide B from both sides:
[tex]\frac{By}{B}[/tex] = [tex]\frac{C - Ax}{B}[/tex]
y = [tex]\frac{C - Ax}{B}[/tex]
Finally, to get an equivalent answer for an answer choice, divide each term by B on the right side of the equation:
y = [tex]\frac{C}{B}[/tex] - [tex]\frac{Ax}{B}[/tex]
or
y = -[tex]\frac{Ax}{B}[/tex] + [tex]\frac{C}{B}[/tex]
or
y = [tex]\frac{-Ax}{B}[/tex] + [tex]\frac{C}{B}[/tex]
This answer is the same as answer choice D, and so D is the correct answer.
Answer: D.
Step-by-step explanation:
[tex]Ax+By=C\\Ax+By-Ax=C-Ax\\By=C-Ax\\[/tex]
Divide both parts of the equation by B:
[tex]\displaystyle\\y=\frac{C-Ax}{B} \\\\y=\frac{C}{B}-\frac{Ax}{B} } \\\\y=-\frac{Ax}{B} +\frac{C}{B}[/tex]
Which graph best represents Sarah total earnings for babysitting
Answer:
Sarah earned $10 per hour for babysitting
Step-by-step explanation: