Taxes are not deducted for gross income.
Roderick's gross income for 6 months = $3,204.17 × 6 = $19,225.02
Wife's gross income for 6 months = $25.07 × 37.5 × 26 = $25,057.5
Total gross income = $44,282.52
3v+4(v-2)= -29 solve for v
Answer:
v = -3
Step-by-step explanation:
1) Expand.
3v + 4v - 8 = -29
2) Simplify 3v + 4v - 8 to 7v - 8.
7v - 8 = -29
3) Add 8 to both sides.
7v = -29 + 8
4) Simplify -29 + 8 to -21.
7v = -21
5) Divide both sides by 7.
v = -21/7
6) Simplify 21/7 to 3.
v = -3
A number written in the form a + bi is called a _____ number.
A. Discriminant
B. Quadratic
C. Complex
D. Linear
Answer: A. Complex
Step-by-step explanation: hope this helps!
NO LINKS!! Jacob just won $32000 on the new game show, "The Wall,". He invested his winnings at an interest rate of 4.5%, compounded quarterly.
Answers:
a) See the table below
b) The equation is [tex]y = 32000(1.01125)^x[/tex]
c) $40,024.02
d) See the graph below
=========================================================
Explanations:
a)
Start with part (b) where I detail how to get the equation.
Once the equation is found, plug in x = 0 to get
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^0\\\\y = 32000\\\\[/tex]
Repeat for x = 1
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^1\\\\y = 32360\\\\[/tex]
Repeat for x = 2, x = 3, x = 4 and x = 20 to get the table shown below.
-----------------------
b)
The template for any exponential equation is [tex]y = a(b)^x[/tex]
a = starting amount = 32000
b = growth factor
The annual interest rate is 4.5%
We compound quarterly, so the quarterly rate is (4.5%)/4 = 1.125% which converts to the decimal form 0.01125; adding one to this leads to the growth factor of b = 1.01125
We go from [tex]y = a(b)^x[/tex] to [tex]y = 32000(1.01125)^x[/tex]
-----------------------
c)
Plug in x = 20 to represent 20 quarters have elapsed (aka 20/4 = 5 years)
[tex]y = 32000(1.01125)^x\\\\y = 32000(1.01125)^{20}\\\\y \approx 32000(1.25075052084381)\\\\y \approx 40024.016667002\\\\y \approx 40024.02\\\\[/tex]
The investment would be worth $40,024.02 after five years, aka twenty quarters.
-----------------------
d)
See below for the graph. I'm using GeoGebra to make the graph. Another option is Desmos. It's preferable to use technology than to graph by hand. If you wanted to graph by hand, then you'd plot each of the points found in the table. Then draw a curve through all those points.
Answer:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)n = number of compounding periods per unit of timet = time in decimal years (e.g. 6 months = 0.5 yrs)Given:
P = $32,000r = 4.5% = 0.045n = 4 (compounded quarterly)t = 0.25x[tex]\implies y=32000(1+\frac{0.045}{4})^{4 \times 0.25x}[/tex]
[tex]\implies y=32000(1.01125)^x[/tex]
Part (a)[tex]\begin{tabular}{|c | c |}\cline{1-2} \bf Quarterly & \bf \$ \\\cline{1-2} 0 & 32000.00\\\cline{1-2} 1 & 32360.00\\\cline{1-2} 2 & 32724.05\\\cline{1-2} 3 & 33092.20\\\cline{1-2} 4 & 33464.48\\\cline{1-2} --- & --- \\\cline{1-2} 20 & 40024.02\\\cline{1-2}\end{tabular}[/tex]
Part (b)[tex]y=32000(1.01125)^x[/tex] (where x is the number of quarterly periods)
Part (c)$40,024.02
Part (d)see attached
50 points each question. Please help. How do I solve?
Answer:
I'm not sure if it's correct
A cyclist rides 24 miles at an average speed of 9 miles per hour. At what rate must the cyclist cover the next 20 miles in order to bring the overall average speed up to 12 miles per hour? The cyclist must ride at 00 miles per hour.
Answer:
20 m/hr
Step-by-step explanation:
distance / rate = time
24 miles / 9 miles/hr = 2 2/3 hr
(24 + 20 miles) / 12 miles/hr = 3 2/3 hr
3 2/3 - 2 2/3 = 1 hour to ride the next 20 miles means 20 m/hr
What number is represented by point P? State your answer in scientific notation
and in standard form.
Answer:
5.7×10^-30.0057Step-by-step explanation:
Point P is marked in the expanded view on the 7th mark of the 10 marks between 5×10^-3 and 6×10^-3. That means it is representing ...
(5 +7/10)×10^-3 = 5.7×10^-3 . . . . scientific notation
__
The -3 exponent of 10 means the multiplier of the value is 1 in the 3rd place to the right of the decimal point: 0.001. So, the standard form of the number is ...
5.7×0.001 = 0.0057 . . . . . standard form
How do I do this question?
Answer:
Step-by-step explanation:
you can think of it backwards,
-50 = 3x - 8y
x = 6y
X x 3 = 3x
6y x 3 = 18y
3x = 18y
18y - 8y = -50
10y = -50
y = -5
6 x -5 = -30
x = -30
The pentagonal prism below has a base area of 38 units? and a height of 7.4 units.
Find its volume.
270.4
278.4
281.2
294.2
281.2 units³
volume of Prism: Base Area x Height
Here given:
Base Area: 38 units²
Height: 7.4 units
Solve for volume:
38 x 7.4
281.2 units³
Volume:-
Area of base×Height38(7.4)2812/10281.2units²Function or Not a Function
Step-by-step explanation:
problem 10 is function
but problem 9 is not
simplify. giving brainliest :D
show steps in a simple way (not to long of an example ty :))
Answer:
- 3/2 x²y
Step-by-step explanation:
Multiply the numbers and constant separately.
constant means x any y.
( - 2/3 x ) ( 9/4 xy )
- 2/3 * 9/4 * x * xy
= ( - 2/3 * 9/4 ) * ( x * xy )
= ( - (2*9)/(3*9) ) * ( x²y )
= ( - 18/12 )* x²y
= - 3/2 x²y
Write the ratio as a ratio of whole numbers in lowest terms
$0.90 to $0.60
Answer:
3:2
Step-by-step explanation:
If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.
for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60
using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:
0.9/0.6 = 1.5
1.5 x 2 = 3
this gives 3/2 = 1.5
so we know that the ratio is 3:2 and this is the smallest whole number that it could be
A book sold 33,100 copies in his first month of release suppose is represents 7.6% of the number of copies sold to date how many copies have been sold to date?
Answer:
2515 number of copies sold to date
My book has 120 pages. If I have read half of it how many pages have I read
Answer:60 pages
Step-by-step explanation:
first take away the zero then devide by 2 then add the zero the the number that your left with.
Triangle ABC and DEF are similar which proportion is true
The length of DE in centimetres is 12 .
The following proportion can be established as follow:
AB / DE = BC / EF = AC / DF
Therefore,
let's find DE as follows;
AB / DE = BC / EF
4 / DE = 3 / 9
cross multiply
9 × 4 = 3DE
divide both sides by 3
DE = 36 / 3
DE = 12 cm
learn more: https://brainly.com/question/22808925?referrer=searchResults
find all the fraction between 0 and 1
Answer:
Between 0 and 1 there is 12, between 1 and 2 there is 112=3/2, and so on. In fact, there are infinitely many fractions between any two whole numbers. Let's see why. Between 0 and 1 there are also 13, 14, 15, and any number that can be written as 1n where n is some whole number.
__________________
Hope this helped! Have a nice day!
Please give Brainliest when you can.
__________________
-Dont let the Pirates get ya!
-Jaron, King of Carthya.
Kevin and randy muise have a jar containing 52 coins. all of which are either quarters or nickels. the total value of coins is $6.40. how many of each coin do they have?
Answer:
19 quarters33 nickelsStep-by-step explanation:
For mixture problems, it is convenient to let the variable represent the quantity of the high-value contributor.
Here, we can let x represent the number of quarters. Then the number of nickels is (52-x), and the total value of the coins is ...
0.25x +0.05(52 -x) = 6.40
0.20x +2.60 = 6.40 . . . . . . . . simplify
0.20x = 3.80 . . . . . . . . . . . subtract 2.60
x = 3.80/0.20 = 19 . . . . divide by the coefficient of x
The number of quarters is 19. The number of nickels is 52-19 = 33.
Suppose that$ 7000 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
Answer:
1) 7420
2) 7865.5
Step-by-step explanation:
The Formula for Compound Intertst is Amout(rate/100+1)^number of years
7000(.06+1)^1
7000(.06+1)^2
What is the equation of the line in slope-intercept form?
Answer:
Step-by-step explanation:
Its a linear function it goes throw the y-x Axis and is in a striaght line.
Answer:
y = [tex]\frac{5}{2}[/tex] x + 5
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = [tex]\frac{5}{2}[/tex] x + 5 ← equation of line
The formula d = 52t+65t can be used to find the distance, d, between two
cars after traveling t hours in opposite directions. After how many hours will
the distance between the two cars be 234 miles?
Answer: t=2
Step-by-step explanation:
add the t's and calculate
In the figure below, triangle QRS is isosceles, with QR SR.
If mSPQ = 36° and mQRS = 32°, what is mPQR?
A.
118°
B.
138°
C.
133°
D.
128°
Answer:
D
Step-by-step explanation:
since Δ QRS is isosceles then the base angles are congruent , that is
∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°
the sum of the 3 angles in Δ SPQ = 180° , then
∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°
Then
∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°
Solve the equation 64x2 − 144 = −23 by using square roots.
x = ±11/8
x = ±3/2
no real solutions
x = ±7/4
Answer:
The answers are:x = ±7/4x = ±3/2x = ±11/8
yww:)
Answer:
Option A, [tex]x =[/tex] ± [tex]11/8[/tex]
Step-by-step explanation:
Step 1: Add 144 to both sides
[tex]64x^2 - 144 = -23[/tex]
[tex]64x^2 - 144 + 144 = -23 + 144[/tex]
[tex]64x^2 = 121[/tex]
Step 2: Divide both sides by 64
[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]
[tex]x^2 = 1.890625[/tex]
Step 3: Square root both sides
[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]
[tex]x =[/tex] ± [tex]1.375[/tex]
[tex]x =[/tex] ± [tex]11/8[/tex]
Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]
Alex eats 2 pieces of candy. Marisol eats 3 times as many pieces of candy as Alex. Which equation can be used to determine the amount of candy that Marisol eats? Let a represent Alex and m represent Marisol.
m=3a
m=3a+2
m=2a
m=2a+3
Answer:
m = 3a
Step-by-step explanation:
The number of pieces of candy eaten by Alex is not important.
The only thing that matters is that Marisol eats 3 times as many pieces of candy.
If a is the number eaten by Andy, then 3 times a equals the number of pieces of candy eaten by Marisol, or m=3a
On the coordinate plane below, what is the length of AB?
Answer:
Ok so i think you can just count it i dont know; edit : i counted, it turns out the answer is 15 :)
Solve for x:
AD bisects BAC
Okay What is the value of x?
Answer:
x=75
Step-by-step explanation:
99/66=1.5
30x1.5=45
30+45 =75
100 POINTS WILL MARK BRAINLIEST DONE BY 9:00 attachment included
Solve the linear equations below. Show ALL your work AND circle the type of solution you found! (10 points)
Answer:
1. No sol.
2. One Sol. x=4
3. One Sol. w=22 1/2
Step-by-step explanation:
1.
Group like terms:
4+3p=6p-3p+5
Add similar elements (6p-3p=3p):
4+3p=3p+5
Subract 4 from both sides:
4+3p-4=3p+5-4
Simplify:
3p=3p+1
Subtract 3p from both sides:
3p-3p=3p+1-3p
Simplify:
0=1
There is no solution.
2.
One Sol. x=4
Switch sides:
3x-2=10
Add 2 to both sides:
3x-2+2=10+2
Simplify:
3x=12
Divide both sides by 3:
3x/3=12/3
Simplify:
x=4
There is a solution.
3.
One Sol. w=22 1/2
Subtract 7 from both sides:
2/3w+7-7=22-7
Simplify:
2/3w=15
Multiply both sides by 3:
3*2/3w=15*3
Simplify:
2w=45
Divide both sides by 2:
2w/2=45/2
Simplify:
w=22 1/2
There is one sol.
Explain how to find 398 + 257 with mental math and with the standard algorithm.
Step-by-step explanation:
If you were to round 398 to the nearest hundred, you would get 400. that's only 2 off of 398. when you add 400 + 257 that would equal 857 because 4 + 2= 6 and then the other two digits on 400 are zeros so 5 and 7 stay the same. with 857, you must now subtract 2 because you added 2 earlier. 857 - 2 = 855.
Help help math math math math
Answer:
(-2,1)
Step-by-step explanation:
The solution of a system of equations is wherever the two lines intersect. So, this is quite easy. We can see they intersect at (-2,1). We can tell it is (-2,1) becuase it is two units left and one units up from the origin.
That is the solution.
(-2,1)
Answer:
The answer is (-2,1). Hope this helps :)
Step-by-step explanation:
Which expression is equivalent to -18a^-2b^5/-12a^-4b^-6
a. 2a^2b^11/3
b. 2a^2b^30/3
c. 3a^2b^11/2
d. 3a^2b^30/2
Answer:
c. 3a^2b^11/2
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
[tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]
Can somebody help me I am a lil confused with the equation
Answer:
a) 7000 x 1.06^t
b) 11156
Step-by-step explanation:
a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.
b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.
CAN SOMEBODY HELP ME PLEASE
Answer:
vertex (3, -1)y-intercept: (0, 8)x-intercepts: (2, 0), (4, 0)Step-by-step explanation:
You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.
__
VertexThe vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).
Y-interceptThe y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).
X-interceptsThe x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).
__
Additional comment
The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.