The future value of Danielle's account in 3 years given the amount invested monthly and the APR is $1909.06.
What is the future value of the account?The formula that can be used to determine the future value of the annuity is: monthly deposits x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 4%/12 n = number of years = 3 x 12 = 36$50 x [(1.003333^36) - 1] / 0.003333 = $1909.06
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Help me answer this question about congruent triangles. 50 points available.
Answer:
B
Step-by-step explanation:
No these triangles are not congruent.
Left triangle
Shortest side = 6 cm
Longest side = 13 cm
3rd side = unknown but < 13
Right triangle
Shortest side = 6 cm
Longest side = unknown but > 13
3rd side = 13 cm
Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.
We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.
What is the length of side a? Round to the nearest tenth
Answer:
○ [tex]\displaystyle 12,9[/tex]
Step-by-step explanation:
Use the Law of Sines to find the length of the second edge:
Solving for Angles
[tex]\displaystyle \frac{sin\angle{C}}{c} = \frac{sin\angle{B}}{b} = \frac{sin\angle{A}}{a}[/tex]
Use [tex]\displaystyle sin^{-1}[/tex]towards the end or you will throw your result off!
Solving for Edges
[tex]\displaystyle \frac{c}{sin\angle{C}} = \frac{b}{sin\angle{B}} = \frac{a}{sin\angle{A}}[/tex]
Let us get to wourk:
[tex]\displaystyle \frac{a}{sin\:40} = \frac{10}{sin\:30} \hookrightarrow \frac{10sin\:40}{sin\:30} = x; 12,855752194... \\ \\ \boxed{12,9 \approx x}[/tex]
I am joyous to assist you at any time.
please ifs due today!!
You place some money in a savings account the savings account earns 2% simple interest. explain how you can find the interest earns after x years.
From the tip of a 9 foot tree, to the end of it's
shadow is 15 feet. Which is longer, the tree
or the shadow? By how much?
Answer:
The shadow is longer by 3ft
Step-by-step explanation:
A simple a^2 + b^2 = c^2 problem
81 + b^2 = 225
b = 12ft
A path of 0.5 meter wide runs round within a square garden of side 15 m.Find it's perimeter ?
Answer:
:))
Step-by-step explanation:
Rhys's house had a temperature of 12°C. He put the heating on and the temperature rose by 8°C. As he was still co Rhys decided to light a fire which increased the temperature by a further 13°C. What was the temperature in the hou now?
Answer:
this is very easy.
Step-by-step explanation:
if he started at a temperature of 12, then added 8 and added 13 onto that? the sum of those numbers would be 33. so 33 degrees Celsius
Write a quadratic function f whose zeros are -3
Answer:
x2 - x - 12 is the Quadratic Polynomial Whose zeroes are -3 and 4.
Find the value of x.
A. 53°
B. 72°
C. 39°
D. 48°
Answer: 53
Step-by-step explanation:
In ΔWXY, y = 8.6 cm, x = 8.5 cm and ∠X=100°. Find all possible values of ∠Y, to the nearest 10th of a degree.
The possible value of ∠Y to the nearest tenth of a degrees in triangle WXY is 85.1 degrees.
How to find angle of a triangle using sine rule
Let's find angle Y using sine rule,
Hence,
x / sin X = y / sin Y
where
x = 8.5 cmy = 8.6 cm∠X = 100°8.5 / sin 100° = 8.6 / sin Y
cross multiply
8.5 sin Y = 8.6 sin 100°
sin Y = 8.6 sin 100° / 8.5
sin Y = 8.4693466759 / 8.5
Y = sin ⁻¹ 0.99639372657
Y = 85.1325941735
∠Y = 85.1°
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Which of the following is true about the decimal form of the number? 25/225
A It is neither a terminating decimal nor a repeating decimal.
B It is both a terminating decimal and a repeating decimal.
C It is a repeating decimal
Answer:
I think it's B because it stops but keeps going.
Step-by-step explanation:
Help I don't knoz if this is right but I think the answer is d
What value of x makes this inequality true?
x - 16 < 43
Answer:
read below
Step-by-step explanation:
x - 16 < 43
there are many values that can make it true
pretty much any number that can have 16 subtracted from it and be less than 43 will work.
or any number less than or equal to 43.
for example:
34-16<43
↓
18 < 43
P = $700, r = 5%, t = 8 years; compounded quarterly
HELP ME ASAP!!!
Answer:
$1,041.69
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation:
Forumla; P(1 + r/n)nt
700.00(1 + 0.05/4)(4)(8)
700.00(1 + 0.0125)(32)
$1,041.69
hope this helps!
Answer:
$1,041.69
Step-by-step explanation:
Compound interest formula: [tex]A=P(1+\frac{r}{n})^{nt[/tex]
A = amount (future value ($))
P = principal (orignal amount - $700)
R = rate (written as a decimal - 5%/100= 0.05)
N = compound (quarterly - 4) 4 quarters in 1 yr.
T = number of years (8)
[tex]A=P(1+\frac{r}{n})^{nt[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=700(1+\frac{0.05}{4})^{4*8} < == start\ from\ the\ parenthesis\ and\ divide\ first\\\\A=700(1+0.0125)^{4*8} < == add\ the\ \#s\ in\ the\ parenthesis\\\\A=700(1.0125)^{4*8} < == multiply\ the\ exponents\\\\A=700(1.0125)^{32} < ==multiply\\\\A=700(1.488131) < ==multiply\\\\A=1041.691\\\\A=$1,041.69[/tex]
Hope this helps!
How far is 75% of a 2,000-kilometre trip?
Answer:
1500
Step-by-step explanation:
Simply multiply 0.75 by 2000 to get the percent of the trip, 1500. Hope this helps!
What fraction is equivalent to four tenths and has a denominator of 100?
Answer:
[tex]\frac{40}{100}[/tex]
Step-by-step explanation:
You can multiply on the upper and bottom part by the same number without changing the fraction so [tex]\frac{4}{10}=\frac{4\cdot 10}{10\cdot 10}=\frac{40}{100}[/tex]
Identify the set as finite or infinite.
{1, (1/4), (1/16), (1/64), ...}
ZA and ZB are vertical angles. If mA = (2x - 4)º and mZB = (4x - 30),
then find the value of x.
Answer:
x=13
Step-by-step explanation:
2x-4 = 4x - 30
-4 = 2x - 30
26 = 2x
x = 13
Some college friends have decided to go on a road trip over the summer with some friends. Finances are tight and they need to hire a car for the trip. There are two hire companies to choose from: Crazy Curly's charges a base fee of $20 and then 30 cents per mile. Bill's Beauties charges 20 cents per mile and a base fee of $50. - Write a system of equations that can be used to determine at what trip distance Bill's and Curly's rental cost would be the same. - At what trip distance would Bill's and Curly's rentals cost the same amount?
Answer:
300 milesStep-by-step explanation:
Let
y- the amount of charge, x - the number of milesThe equations as per question are below
Crazy Curly's
y = 0.3x + 20Bill's Beauties
y = 0.2x + 50Solve the system by substitution
0.3x + 20 = 0.2x + 500.3x - 0.2x = 50 - 200.1x = 30x = 30/0.1x = 300
what are the features of function g if g(x)=f(x + 4) + 8?
vertical asymptote of x= -4
domain of (4, [infinity])
y-intercept at (0,10)
x-intercept at (1,0)
range of (8, [infinity])
The correct statement is that the range of the function is (8, [infinity])
How to find the intercept, domain and range of a functionGiven the function as shown below:
g(x) = √(x + 4) + 8
The domain of the function is the point here x + 4 ≥ 0
Domain = x ≥ -4
In interval form, the domain of the function is [-4, 0)
The range of the function is the real values from 8 and above. Hence the range of the function is (8, [infinity])
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According to the Graffalo the slope line B is ?:
Answer:
yes ikr
Step-by-step explanation:
yes ikr
yes ikr
yes ikr
yes ikr
yes ikr
yes ikr
yes ikr
yes ikr
yes ikr
Explain how to determine if the two expressions are equivalent using x = 6 and x = 10. 8x 40 8(x 5)
The two expressions are equivalent, which gives the same values at x=6 and x=10 when put the values of x and compare them.
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given expressions are,
[tex]8x +40[/tex]
[tex]8(x+ 5)[/tex]
It has to determine if the two expressions are equivalent using x = 6 and x = 10.
The value of the first equation at x=6 are,
[tex]8x +40=8(6)+40\\8x +40=48+40\\8x +40=88[/tex]
The value of the first equation at x=10 are,
[tex]8(10) +40=80+40\\8(10) +40=120[/tex]
Now, the value of the second equation at x=6 are,
[tex]8[(6)+5]=48+40\\8[(6)+5]=88[/tex]
Similarly, the value of the second equation at x=10 are,
[tex]8[(10)+5]=80+40\\8[(10)+5]=120[/tex]
The values of both equation are same at x=10 and x=6.
Hence, to determine, the two expressions are equivalent using x = 6 and x = 10, put the values of x and compare the values.
Learn more about the equivalent expression here;
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4. Find the perimeter of the figure below. Use 3.14 for pi.
number answer.
Answer:
90.24 mm
Step-by-step explanation:
Circumference = 2πr
C = 2(3.14)(16)
C = 100.48 mm
Perimeter of the figure = 20 + 20 + 1/2 (circumference)
P = 40 + 1/2 (100.48)
P = 40 + 50.24
P = 90.24 mm
I hope this helps!
100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −2; (−2, 83) x = −4; (−4, −11)
Let's see
[tex]\\ \rm\rightarrowtail y=6x^2-25x+11[/tex]
Graph attached
vertex(-2,-13)Axis of symmetry
x=-2Answer:
axis of symmetry: x = 2
vertex: (-2, 13)
Step-by-step explanation:
Given function
[tex]\sf y=6x^2-24x+11[/tex]
Vertex form
[tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Expand vertex form:
[tex]\sf \implies y=ax^2-2ahx+ah^2+k[/tex]
Compare coefficients of expanded vertex form with given function:
coefficient of [tex]\sf x^2[/tex]:
⇒ a = 6
coefficient of [tex]\sf x[/tex]:
⇒ -2ah = -24
⇒ ah = 12
⇒ 6h = 12
⇒ h = 2
constant:
⇒ [tex]\sf ah^2+k=11[/tex]
⇒ [tex]\sf 6 \cdot 2^2+k=11[/tex]
⇒ [tex]\sf 24+k=11[/tex]
⇒ [tex]\sf k=-13[/tex]
Vertex
Vertex = (2, -13)
Axis of symmetry
Axis of symmetry is when x = h
Therefore, axis of symmetry is x = 2
Please help me with this equation, add process too. Thanks
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
Let's solve ~ ☂
[tex]\qquad \sf \dashrightarrow \: - 0.6(m + 1) = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - (m + 1) = 3 \div 0.6[/tex]
[tex]\qquad \sf \dashrightarrow \: - (m + 1) = 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - m - 1= 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 5 + 1[/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: m = - 6[/tex]
I hope it helps ~
PLEASE HELP!!!!!!!!!
Answer:
114
Step-by-step explanation:
The external angle measure is equal to the half of difference between the larger intercepted arc (5x-12) and the smaller intercepted arc (3x)
32 = (5x-12 -3x)/2
combine like terms in parenthesis and multiply both sides by 2
32·2 = 2x-12
multiply 32·2 = 64, and add 12 to both sides
64 + 12 = 2x
add 64+12 = 76, and divide both sides by 2 to isolate x
76/2 = x
38 = x
The measure of arc AB is 3x.
Substitute x for 38
Measure of arc AB = 3x = 3·38 = 114
Two rectangles share a common side as shown.
Determine whether each expression can be used to determine the
total area, in square feet, of the two combined rectangles.
ft
Select Yes or No for each expression.
7.52 + 20
o Yes
Ο Νο
*
7.5 ft
x ft
27.5 + 2
Yes
Ο Νο
20 (7.5 + x)
o Yes
Ο Νο
150 + 3
Yes
Ο Νο
202 + 150
O Yes
No
Answer:
yes they are
Step-by-step explanation:
integration of csc^2(9x)dx
[tex]\displaystyle \int csc^2(9x) dx \\\\=\dfrac 19\displaystyle \int \csc^2 u ~du~~~~~~~;\left[\text{Let}~u= 9x \implies dx = \dfrac{du}9\right]\\\\=-\dfrac 19 \cot u + C\\\\=-\dfrac 19 \cot(9x)+C[/tex]
A right square pyramid is shown.
The height is 10 centimeters and the side length of the base is 16 centimeters. What is the length, in centimeters (cm), of s?
Given the height and the side length of the square pyramid, the length of s is 12.81 cm.
What is the length of s?A square pyramid is a three-dimensional object that is made up of a square base and four triangular bases that are joined together at a vertex.
S in the diagram represents the slant height of the square pyramid.
The formula that can be used to determine the slant height is:
s² = r² + h².
Where:
r = side length / 2 = 16/2
s = √8² + 10²
s = 12.81 cm
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Kristen drank 7 cups of orange juice in the morning and 1/4 of a cup in the afternoon. How much orange juice did Kristen drink in all?