The following are the characteristics of the graph of the linear parent function:
B. It has a slope of 1.
C. It is a parabola.
D. It is a straight line.
Lets explain the meaning of linear parent function
- A linear parent function is the equation y = x or f(x) = x
- A parent function is the simplest equation of a function
- It represented by a straight line passing through the origin point O
- The x-coordinate and the y-coordinate of any points lie on it are equal
- The slope of the line is 1 because the slope is the change of Δy/Δx
and Δy = Δx
The characteristics of the graph of the linear parent function are
∵ Linear parent function is f(x) = x and f(x) = y
∴ x = y
∵ The slope = Δy/Δx
∵ Δx = Δy because x = y
∴ The slope of it is 1
B. It has a slope of 1
∵ y = 0
∵ If x = 0 then y must = 0
∴ It goes through the origin
C. It goes through the origin
∵ It is a linear function
∵ All linear function represented by a straight line
∴ The graph of the linear parent function is a straight line
D. It is a straight line
Hence we get the right answers.
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What is does y = 3x - 4
Answer:
x = y/3 + 4/3
Step-by-step explanation:
Solve for x:
y = 3 x - 4
y = 3 x - 4 is equivalent to 3 x - 4 = y:
3 x - 4 = y
Add 4 to both sides:
3 x = y + 4
Divide both sides by 3:
Answer: x = y/3 + 4/3
The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.
Answer: base = 23 height = 31
Step-by-step explanation:
Area of triangle = (bh)/2
A = 356.5 cm2
h = b+8
356.5 = (b(b+8)) / 2
2(356.5) = b2 + 8b
0 = b2 + 8b - 713
Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)
b = -31 , 23
23 is the base 23 + 8 = 31 = height
PEMDAS Simplify using order of operations.
7 + 3 x 5
Answer: 22
Step-by-step explanation:
3 times 5 then add 7
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?
PLEASE HELP
24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
According to the question,
We have the following information:
The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.
Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
So, we have:
x+y = 40
x = 40-y ...(1)
55x/100+80y/100 = 40*65/100
55x+80y = 40*65
Putting the value of x from equation 1:
55(40-y)+80y = 2600
2200-55y+80y = 2600
2200+25y = 2600
25y = 2600-2200
25y = 400
y = 400/25
y = 16 pints
Putting this value in equation 1:
x = 40-y
x = 40-16
x = 24 pints
Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
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P(H)=
P(T)=
let me know if you know how to do this
After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.
As given in the question,
After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,
Number of total outcomes = { H , T }
Total number of outcomes = 2
Number of favourable outcomes to represent heads = 1
Number of favourable outcomes to represent tails = 1
Probability =(Number of favourable outcomes)/ (Total number of outcomes)
Probability of getting heads from the total outcomes is equal to
P(H) = 1 / 2
Probability of getting tails from the total outcomes is equal to
P(T) = 1/2
Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.
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Pratap Puri rowed 18 miles down a river in 2 hours, but the retum trip took him 4 hours. Find the rate Pratap can row in still water and find the rate of the current. Let x=rate Pratap can row in still water and y=rate of the current
What is the rate that Pratap rows in still water?
Pratap can row at a rate of____?
(Type an integer or a decimal)
in still water.
Rate Pratap can row in still water is 6.75 and Rate of current is 2.25
Step: 1
Let's y = speed of water and x = his speed of rowing in still water
Speed = Distance/Time (or)
Rate = Distance/Time
Step: 2
he row downstream in 2 hours
Rate in downstream = 18/2
Rate in downstream = 9
i.e.
x + y = 9
x = 9 - y ---(i)
Now, time taken by min to row in upstream = 4 hours
Rate in upstream = Distance/Time = 18/4
Rate in upstream = 4.5
i.e., x-y = 4.5 ---(ii)
Putting the value of x from equation (i) in equation(ii)
9 - y - y = 4.5
9 - 2y = 4.5
9 - 4.5 = 2y
y = 4.5/2
y = 2.25
Putting the value of y in equation (ii)
x - 2.25 = 4.5
x = 4.5 + 2.25
x = 6.75
x = Rate Pratap can row in still water = 6.75
y = Rate of current = 2.25
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How MANY THOUSANDTHS IN 0.1?
Answer:
100
Step-by-step explanation:
.001*100=.1
Answer:
100 thousandths
Step-by-step explanation:
If cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following. Use fractions and radicals only, no decimals.
sin(x/2)=
cos(x/2)=
tan(x/2)=
please help
According to the trignonmentry of half angles, the value of sin(x/2) is √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)
Trigonometry of half angles
Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.
Given,
Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.
sin(x/2), cos(x/2), tan(x/2).
According to the concepts in trigonometry,
We know that the following formulas.
=> sin(x/2) = √(1-cosx)/2
=> cos(x/2) = √(1+cosx)/2
=> tan( x/2)=sin x/1+cosx
Here we know that cos (x) = 5/6
Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is
Therefore, we can calculate the value of the adjacent a as,
=> a = √(6²-5²)
=> a = √36-25
=> a= √11
Therefore the value of sin x= √11/6
So, the value of sin(x/2)= √(1 - 5/6)/2
And the value of cos(x/2)= √(1 + 5/6)/2
Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)
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Can you please help me
How to find the vertex?
The general form of an absolute value function:
y = a|x - h| + k, where (h, k) is vertex and a - coefficientGiven function is:
y = |x + 3| - 2Its vertex is (- 3, - 2), this is our first point to plot, point A.
Step 2How to find x-intercepts?
Set y = 0 and solve for x:
|x + 3| - 2 = 0|x + 3| = 2x + 3 = 2 and x + 3 = - 2x = - 1 and x = - 5So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.
Step 3Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.
Can someone please help me with this??
Answer:
3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )
..
A scale drawing of a rectangular bedroom is shown below. Using a scale of 1cm=4 feet, enter the actual area of the bedroom in square feet.
Answer:
Below
Step-by-step explanation:
Need the drawing but take the two cm measurements and multiply them together then multiply by 4 and then multiply by 4 again to get ft^2
Translate The product of the quotient of a and b and the quotient of c and d
The product of the quotient of a and b and the quotient of c and d is ac/bd.
What is a quotient?In mathematics, a quotient simply means a quantity produced through the division of two numbers.
From the information, the product of the quotient of a and b and the quotient of c and d.
The product will be:
= a/b × c/d
= ac / bd
The product is ac/bd.
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Can anyone help?? Question is attached!
Answer:
9.37
Step-by-step explanation:
twelve surgeons
112.44 / 12 = 9.37
Answer:
$9.37
Step-by-step explanation:
112.44 ÷ 12
select all the expressions equivalent to 4^10
The expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe need to find all the expressions equivalent to 4^10.
We will use laws of exponents for all the options one by one.
Option A:
2^5 . 2^2 = 2^(5 + 2) = 2^7
This is not equivalent to 4^10.
Option B:
2^10 = 2^(2 * 10) = (2^2)^10 = 4^10
This is equivalent to 4^10.
Option C:
4^4 . 4^6 = 4^(4 + 6) = 4^10
This is equivalent to 4^10.
Option D:
4^7 . 4^-3 = 4^(7 + (-3)) = 4^4
This is not equivalent to 4^10.
Option E:
4^4 / 4^-6 = 4^(4 - (-6)) = 4^10
This is equivalent to 4^10.
So, 2^20, 4^4 . 4^6, and 4^4 / 4^-6 are equivalent to 4^10.
So, option B, option C, and option E are correct.
Thus, the expressions equivalent to 4^10 are 2^20, 4^4 . 4^6, and 4^4 / 4^-6. Option B, option C, and option E are correct.
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Anita works a part time job where she makes 9.45$ per hour Anita’s gross pay for the current period is $238.61 her deductions include $28.63 for federal taxes 14.79 for social security 3.46 for Medicare 10.14 for state taxes . How many hours did Anita work and what was her net pay ? Anita works 31 hours next week what is her gross pay total amount of deductions and net pay assuming the same percentage is taken out for each deductions during the next pay period ?
For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.
When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.
As given in the question,
a. Anita get pay per hour = $9.45
Gross pay received by Anita = $238.61
Deductions :
Federal tax = $28.63
Society tax : $14.79
Medicare : $3.46
State tax : $10.14
Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )
= $57.02
Net pay = Gross pay - total deduction
= $ ( 238.61 - 57.02 )
= $ 181.59
Let us consider Anita works for 'h' hours at the rate of $9.45,
9.45h = 238.61
⇒ h = 238.61/ 9.45
⇒ h = 25.25 hours
b. When Anita works for 31 hours
Her gross pay = 31 × 9.45
= $ 292.95
Deductions are same
Net pay = $ ( 292.95 - 57.02 )
= $ 235.93
Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.
When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.
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In the football club, 36 footballers are Latvians, while there are 4 times less footballers of other nationalities. How many total athletes does the football club have?
Answer:
45
Step-by-step explanation:
Number of Latvian footballers(n¹) = 36
Numer of footballers of other nationalities(n²)=36/4=9
Now total number of footballers= n¹+n²= 36+9 =45
Sam opened a money-market account that pays 4% simple interest. He started the account with $7,000 and made no further deposits. When he closed the account, he had earned $560 in interest. How long did he keep his account open? A. 2 years B. 5 years C. 4 years D. 3 years
the answer is 2 years
Answer:2 years
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is 2 years
NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!
x=-3.645 and x=1.645 is the solution for the given inequality.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given inequality is
y<x²+2x-6
a=1, b=2, c=-6
x=-b±√b²-4ac/2a
=-2±√2²-4(1)(-6)/2(1)
=-2±√4+24/2=
=-2±√28/2=
=-2+√28/2
=-2+5.29/2
=1.645
and -2-5.29/2
x=-3.645
Hence x=-3.645 and x=1.645 is the solution for the given inequality.
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Find the scale of a map if 4.2 cm on the map corresponds to an actual distance of 6.2 km.
Answer:
21/3100000 ≈ 1/147619
Step-by-step explanation:
You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.
ScaleThe scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...
4.2 cm : 6.2 km
or, we can reduce it to ...
2.1 cm : 3.1 km
Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...
1 cm : 1.47619 km
FractionAnother way to write the scale of a map is as a fraction.
(4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000
When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...
≈ 1/147619 . . . . map scale
The scale of the map is ...
21/3100000 ≈ 1/147619 or 2.1 cm : 3.1 km or ≈ 1 cm : 1.47619 km
__
Additional comment
You may need to round the answer to match one of your answer choices.
<95141404393>
Write the equation of the line that passes through
the points (-6,-3) and (2, 0). Put your answer in
fully simplified point-slope form, unless it is a
vertical or horizontal line.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]
My answer and step by step explanation is provided as an attachment.
graph y= absolute value of 5x
The graph of the absolute value function is attached below.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
The absolute value measures the distance of a point x to the origin, hence, for example, |-4| = |4| = 0, and has vertex(turning point) at (0,0).
We have to grpah the absolute value function of y = 5x.
Thus, the function is linear function.
The graph of the function is attached below.
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You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $36, otherwise you lose $30. What is your expected value for the game?
The expected value for the game is -12.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
The probability of rolling a 2 or 5:
= P(2 or 5)
= 1/6 + 1/6 = 1/3
The probability of not rolling a 2 or 5:
= 1 - 1/3
= 2/3
The expected return:
= (1/3)(36) + (2/3)(-36)
= 12 - 24
= -12
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If 3 oranges cost $1.75,how much would 20 oranges cost?
Answer:$12
Step-by-step explanation:
1.75/3= 0.6 (1dp)
0.6 x 20 = 12
Answer:
$11.67
Step-by-step explanation:
3 oranges = 1.75
1 orange = 0.58333333333
20*0.58333333333 = 11.6666667
A book sold 41,900 copies it’s first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date? Round your number to the nearest whole number.
Marcus is on an Olympic training programme.
As part of the programme, he has to have a
blood test and a fitness test at regular
intervals.
Marcus has a blood test every 42 days and a
fitness test every 44 days.
On the day before the training programme
started, Marcus had a blood test and a fitness
test.
After how many days will he next have a blood
test and fitness test on the same day?
Answer:
Step-by-step explanation:
so if it takes 42 days and 44 days just add them up
42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418
44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus
just keep going
what is the value of f(2) when given f(x)=4x+12
There is a pair of natural numbers whose sum is 52 and whose product is 667. The positive difference of their reciprocals is __
The positive difference the numbers is given as 6.
What is the positive difference of their reciprocals ?We are told here that there is a pair of natural numbers whose sum is 52 and whose product is 667. We have to make use of the idea of simultaneous equations to obtain the numbers.
Let the numbers be x and y thus we have;
x + y = 52 ---- (1)
xy = 667 ------ (2)
x = 52 - y ------ (3)
Substituting (3) into (2)
(52 - y)y = 667
52y - y^2 = 667
y^2 - 52y + 667 = 0
Solving the quadratic equation we have;
y=23 or y=29
The difference between the numbers then becomes 29 - 23
= 6
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Seth is planning a route for a train that travels at a constant rate of 220 kilometers per hour.
They want to write an equation that shows how many hours (t) a trip takes in terms of the trip's
distance (d).
t = d/220 is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).
Define the relationship between distance, speed, and time.Speed is calculated as follows: speed = distance/time. Calculating the units for speed requires knowledge of the units for both time and distance. Since the distance is measured in meters (m) and the time is recorded in seconds, the units in this example will be meters per second (m/s) (s).
Let the distance be d and the time is t.
The given speed of the train = 220km/hr
Time = d/speed
t = d/220
This is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).
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Answer: t=220/b
Step-by-step explanation: Khan Academy said so
I really need help 30 pointssss
Answer:
2nd one is the best division
Consider the equation below 5(3a - 1) - 2(3a + 2) = 3(a + 2) + v select two expressions that are equivalent to v
The two expressions equivalent to v are:
5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v6a - 15 = vHow to find the two expressions equivalent to v?Here we have the equation:
5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v
And we want to find expressions equivalent to v, so to do that, we just need to isolate the variable v in one side of the equation, if we subtract:
3*(a + 2) in both sides we will get:
5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v
5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v
That is one of the equivalent expressions, to get the other, we can just simplify the left side.
5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v
15a - 5 - 6a - 4 - 3a - 6 = v
Now we can group like terms:
15a - 6a - 3a - 5 - 4 - 6
6a - 15 = v
That is the other equivalent expression to v.
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