Answer:
The equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0
Step-by-step explanation:
A line is a polynomial function of the first degree that has the following form:
y = m * x + b
where m is the slope of the line and b is the intercept with the Y axis. The slope is the inclination of the line with respect to the abscissa axis.
In this case you know that the slope of line a is ½.
Parallel lines are two or more lines in a plane that never intersect. Two lines are parallel if they have the same slope and different y-intercepts.
You have:
y+½x=2 → y= -½x +2-2x+y+2=0 → y=2x -22x-2=y -½x+y-2=0 → y=½x + 2The line that has the same slope as line a is the last one, so the equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0
7 Alan is self-employed. He earned $22,500 one year and was taxed at
the FICA rate of 15.02%. What was the total amount he had to pay in
FICA taxes?
a. $3,379.50
b. $1,689.75
c. $1,652.20
d. $3,304.40
8 Art is self-employed. He earned $28,500 one year and was taxed at
the FICA rate of 15.02%. What was the total amount he had to pay in
FICA taxes?
a. $2,140.35
b. $4,205.60
c. $2,102.80
d. $4,280.70
9 Edith earns an annual gross salary of $17,500. She has 28% of her
gross salary withheld for taxes and other deductions. What is the net
pay of each paycheck if she is paid weekly?
a. $274.04
b. $43.87
c. $242.31
d. $438.76
10 Nancy earns an annual gross salary of $16,250. She has 26% of her
gross salary withheld for taxes and other deductions. What is the net
pay of each paycheck if she is paid semimonthly?
a. $62.50
b. $541
c. $462.50
d. $501.04
13 Olga deposited $1,500 in a savings account that pays 7.5% interest,
compounded quarterly. What is the balance in her account at the
beginning of the fourth quarter?
a. $1,590
b. $1,560
c. $1,585.97
d. $1,591.81
Answer:
7. A
8. D
9. C
10. D
13. D
Step-by-step explanation:
Hope that helps :)
Find the area and perimeter of the shape below. Show your work.
What is the inverse of the function f(x) = 1/4x - 12?
Oh(x) = 48x - 4
Oh(x) = 48x + 4
O h(x) = 4x - 48
O h(x) = 4x + 48
Happy Holidays! :)
[tex]\large\boxed{h(x) = 4x + 48}[/tex]
[tex]f(x) = \frac{1}{4}x - 12[/tex]
Find the inverse. Begin by swapping the x and y (f(x)) variables:
[tex]x= \frac{1}{4}y - 12[/tex]
Begin isolating for y. Add 12 to both sides:
[tex]x + 12 = \frac{1}{4}y[/tex]
Multiply both sides by 4:
[tex]4(x + 12) = \frac{1}{4}y * 4[/tex]
[tex]4x + 48 = y[/tex]
Therefore:
[tex]h(x) = 4x + 48[/tex]
Name the property that the statement illustrates.
Answer:
Transitive property of segment congruence
Step-by-step explanation:
The reflexive, symmetric, and transitive properties are the criterion for an equivalence relation. In terms of congruence,
The reflexive property states that [tex]\overline{XY} \cong \overline{XY}[/tex] (a segment is congruent to itself)The symmetric property states that if [tex]\overline{AB} \cong \overline{CD}[/tex], then [tex]\overline{CD} \cong \overline{AB}[/tex] (this is essentially commutativity)The transitive property states that if [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\ovelrine{CD} \cong \overline{EF}[/tex], then [tex]\overline{AB} \cong \overline{EF}[/tex].In terms of general equivalence relations,
The reflective property states that [tex]a = a[/tex].The symmetric property states that if [tex]a=b[/tex], then [tex]b=a[/tex].The transitive property states that if [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex].That's the transitive property.
The fact that congruence is transitive means exactly what you have written: if A is congruent to B and B is congruent to C, then you can "bridge" from A to C.
Mia discovered that if she takes half her age and adds 3, it produces the same result as taking one-fourth of her age and adding 7. How old is Mia?
Answer:
she would be 16 years old
Step-by-step explanation:
hope this helps!! :D
From the given information we found out that age of Mia is 16 years.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Mia discovered that if she takes half her age and adds 3,
Assuming Mia's age to be x years.
∴ (1/2)x + 3...(i)
It produces the same result as taking one-fourth of her age and adding 7,
∴ (1/4)x + 7...(ii)
So, (1/2)x + 3 = (1/4)x + 7.
(1/2)x - (1/4)x = 7 - 3.
(1/4)x = 4.
x = 4×4/1.
x = 16.
So, Age of Mia is 16 years.
learn more about linear equations here :
https://brainly.com/question/19549073
#SPJ2
A fraction is which type of number?
Rational or Irrational
Answer:
Rational
Step-by-step explanation:
All rational numbers can be written as fractions.
Please help me out!!!!!
Answer:
Start by identifying which solutions have a degree of 2 Degree of two is the sum of all the exponential powers.You have a coefficient leading of 1 so x^2 would be the correct first term.Hope this helps.16. 8x5 – 16x4 + 8x3
Answer:
it is 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
Once you simplify the equation, you get 40-64+24. When you use 40+24, you get 64 which cancles out the other 64
find all numbers that satisfy the following statement: the square of the number is 5 more then twice the number.
Answer:
I think it is 5 + 2x
Step-by-step explanation:
2)
An Airplane is ascending at a speed of 400 km/hr along a line making an angle of 60' with the
ground. How fast is the altitude of the plane changing?
Answer:
The altitude is changing at a speed of 200 √3 km/hr
Step-by-step explanation:
Here, we want to know how far the altitude of the plane is changing
we are told that the airplane makes an angle of 60 degrees with the ground
So therefore , the rate of change of its altitude will be ;
sin 60 = x/ 400
x = 400 sin 60
x = 400 * √3/2
x = 200 √3 km/hr
The altitude is increasing at a rate of 346.61 km/hr.
The diagram below denotes the given scenario.
Then from the diagram we have,
[tex]sin60^{\circ}=\frac{y}{z}\\\frac{\sqrt{3}}{2} =\frac{y}{z}\\ y=\sqrt{3}\\z=2[/tex]
Then,
[tex]sin\theta =\frac{y}{z}\\cos\theta \frac{d\theta}{dt}\\=\frac{z\frac{dy}{dt}-y\frac{dz}{dt}}{z^2} \\\frac{dy}{dt}=\frac{z^2cos\theta\frac{d\theta}{dt+y\frac{dz}{dt}}}{z}\\\frac{dy}{dt} =\frac{2^2(cos60^{\circ})+\sqrt{3}(400)}{2}\\ \frac{dy}{dt}=346.41 km/hr[/tex]
Learn More:https://brainly.com/question/16086052
Solve for x
If you don’t know how to do it don’t answer
bla nnn,,,,,,bs jfbjnf msnjkmfe sjnmf cmmnefnmv fcve
Answer:
Ummmmm ehhhhhh
I need points for a hw
Nancy had eighty - two dollars to spend on six books. After
buying them she had sixteen dollars. How much did each book cost?
Answer:
11 dollars
Step-by-step explanation:
82-16=66
You subtract the money she has left over and then divide that number by the amount of books that were bought
66 Divided by 6 = 11
which equation represents a line that is perpendicular to line FG
Note: You missed to add some basic information of the perpendicular line or missed the answer options, hence I am solving using a sample equation but it would clear your concept.
Answer:
Please check the attached graph.
Step-by-step explanation:
We know the slope-intercept form of line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given the points
F(1, 8)G(-3, -4)Finding the slope between F(1, 8) and G(-3, -4)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-4\right)[/tex]
[tex]m=\frac{-4-8}{-3-1}[/tex]
[tex]m=3[/tex]
Thus, the slope of the line FG = m = 3
From the given line, we can also determine the y-intercept 'b' by setting x = 0 and checking the corresponding y value.
i.e. at x = 0, y = 5
Thus, y-intercept b = 5
so substituting m = 3 and b = 5 in the slope-intercept form
y = mx+b
y = 3x+5
Therefore, the equation of line FG will be:
y = 3x+5Please check the attached diagram, where the red line represents the line y=3x+5
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.
Slope of Perpendicular line = -1/m = -1/3
Thus, any line with the slope m = -1/3 would be the line that will be perpendicular to line FG
Let say the line with the slope m = -1/3 and y-intercept 2
y = -1/3x + 5
Please check the attached graph, the blue line is representing the perpendicular line y = -1/3x + 5 to line FG
The graph of both lines is clearly representing that the line y = -1/3x + 5 is perpendicular to line FG.
Answer:
Step-by-step explanation:
Island Bank is advertising a special 1.55% APR for long term CDs. Manny takes out a one-year CD for $40,000. The interest is compounded daily. Find the annual percentage yield for Manny's account to the nearest hundredth of a percent. Fill in the blank 1
Answer: 1.55%
Step-by-step explanation:
p = Principal = $40000
r = Interest rate = 1.55% = 0.0155
n = Number of periods = 365
APY = [1 + (r/n)^n - 1]
= [1 + (0.0155/365)^365 - 1]
= [1 + 0.000042)^365 - 1]
= [1.000042]^365 - 1
= 1.015448 - 1
= 1.55%
A meat packer has 180 kilograms of ground meat. He will divide it equally into 50 packages. How much will each package weigh?
Answer:
3.6 kg
Step-by-step explanation:
A meat packer has 180 kilograms of ground meat. He will divide it equally into 50 packages. How much will each package weigh??
Since he is dividing equally, we have:
50 packages = 180 kg
1 package = x kg
Cross Multiply
x kg × 50 packages= 180kg × 1 packages
x kg = 180 kg × 1/50 packages
x kg = 3.6 kg
Hence, 1 package would weigh 3.6 kg(kilograms)
Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at x = 1.
Answer:
The cubic function is f(x) = (27/32)·x - 3/32·x³ - -9/32·x² - 9/32
Step-by-step explanation:
The given function is f(x) = a·x³ + b·x² + c·x + d
By differentiation, we have;
3·a·x² + 2·b·x + c = 0
3·a·(-3)² + 2·b·(-3) + c = 0
3·a·9 - 6·b + c = 0
27·a - 6·b + c = 0
3·a·(1)² + 2·b·(1) + c = 0
3·a + 2·b + c = 0
a·(-3)³ + b·(-3)² + c·(-3) + d = -3
-27·a + 9·b - 3·c + d = -3...(1)
a + b + c + d = 0...(2)
Subtracting equation (1) from equation (2) gives;
28·a - 8·b + 4·c = 3
Therefore, we have;
27·a - 6·b + c = 0
3·a + 2·b + c = 0
28·a - 8·b + 4·c = 0
Solving the system of equations using an Wolfram Alpha gives;
a = -3/32, b = -9/32, c = 27/32 from which we have;
a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0
d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32
The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).
Nate made 8 loaves of bread on Monday and 10 more on Tuesday. He gave an equal number to each of his 9 neighbors. How many loaves of bread did each neighbor receive?
Answer:
2
Step-by-step explanation:
8 + 10 = 18
18/9 = 2
what points do i have to put ? please help
All you have to do is reflect the triangle over the line x = -1.
The answer is in the graph below.
There is a patch of lily pads on a lake. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
Answer:
47 days
Step-by-step explanation:
Since the patch of pads doubles in size every day, the lake would be half covered just one day before it was covered entirely.
jeff has 80 toy cars in his car collection. after his birthday jeff has 94 cars. calculate his percent increase
Answer: 80 - 94
Step-by-step explanation:
PLS HELP ME ANSWER THISSSS
Answer:
WAIT WHERE IS THE QUESTION
Step-by-step explanation:
The net of a triangular prism and its dimensions are shown in the diagram. what is the lateral surface area of the triangular prism in square centimeters
A-264 cm
B-240cm
C-225cm
D “Not here”
Answer: 120 sq in.
Step-by-step explanation:
BRAINLY AND 20 PTS TO WHOEVER GETS IT RIGHT
Answer:
The first one
Step-by-step explanation:
Credit report does NOT state whether borrower will pay loan on time ...though it may give an INDICATION of this
one week ty made (3x + 4) dollars. The following week he made (x + 8) dollars. How much more did he make the first week?
Answer:
(2x – 4) dollars
Step-by-step explanation:
The midpoint of AB is M(-6,-4). If the coordinates of A are (-4,-3), what are
the coordinates of B?
Answer:
(-8,-5)
Step-by-step explanation:
Well, if we divide the square root of M by the hypotenuse due to the activation of the square root of A, then we can achieve the absolute equilibrium between both statements as we bring the oven to about 220 degrees Farenheit, the brownies will look great.
Peyton has p pennies and n nickels. She has at most 18 coins altogether. Write this situation as an inequality.
Answer:
p + n ≠ 18
Step-by-step explanation:
How far can a car travel on 1 gallon of gasoline?
Answer:
25 miles
Step-by-step explanation:
50/2=25
Answer:
25 miles
Step-by-step explanation:
it would be half of 50 so it would be 25 because it goes up by 25 each time
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
The correct format of the question is
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. [tex]P = 400 ( 1.2 )^ t[/tex] Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
(A) 291
(B) 691
(C) 1040
(D) 1440
Answer:
The increase in the population at the end of 2009 is 291 people
Step-by-step explanation:
We are given the equation as [tex]P = 400 ( 1.2 )^ t[/tex]
where
P = No of People
t= No of Years
it is given that in the year 2006 the population is 400
this will only happen when we take t= 0
so for
Year value of t
2006- t = 0
2007- t = 1
2008- t = 2
2009 t = 3
No of people in 2009 will be
[tex]P = 400(1.2)^3[/tex]
= 400*1.728
P = 691.2
Since the equation represents no of people so it can't be in decimals, Therefore the population will be 691
Increase = P(2009) - P(2006)
= 691 - 400
= 291
The increase in the population at the end of 2009 is 291 people.
plz help me i will give you 50 points
Answer: 36
Step-by-step explanation:
First one
Answer:
see below
Step-by-step explanation:
36.196
tens ones. tenths hundredths thousandths
The greatest places is the tens place. We look one place to the right to the ones place. The number in the ones place is 5 or greater so the tens place goes up one place and the ones place becomes a zero
40