Answer:
[tex] \displaystyle a_{1} = 108[/tex]
Step-by-step explanation:
we are given
the sum,common difference and nth term of a geometric sequence
we want to figure out the first term
recall geometric sequence
[tex] \displaystyle S_{ \text{n}} = \frac{ a_{1}(1 - {r}^{n} )}{1 - r} [/tex]
we are given that
[tex]S_n=189[/tex][tex]r=\dfrac{1}{2}[/tex][tex]n=3[/tex]thus substitute:
[tex] \displaystyle 189= \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{1 - \frac{1}{2} } [/tex]
to figure out [tex]a_1[/tex] we need to figure out the equation
simplify denominator:
[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2} } = 189[/tex]
simplify square:
[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2} } = 189[/tex]
simplify substraction:
[tex] \displaystyle \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2} } = 189[/tex]
simplify complex fraction:
[tex] \displaystyle a_{1} (\frac{7}{8} ) \div { \frac{1}{2} } = 189[/tex]
calculate reciprocal:
[tex] \displaystyle a_{1} \frac{7}{8} \times 2 = 189[/tex]
reduce fraction:
[tex] \displaystyle a_{1} \frac{7}{4} \ = 189[/tex]
multiply both sides by 4/7:
[tex] \displaystyle a_{1} \frac{7}{4} \times \frac{4}{7} \ = 189 \times \frac{4}{7} [/tex]
reduce fraction:
[tex] \displaystyle a_{1} = 27\times 4[/tex]
simplify multiplication:
[tex] \displaystyle a_{1} = 108[/tex]
hence,
[tex] \displaystyle a_{1} = 108[/tex]
reduce 12/20 to lowest term
Answer:
3/5
Step-by-step explanation:
12/20
(divide both by 2)
12/2= 6
20/2=10
6/10
(divide by both by 2)
6/2= 3
10/2= 5
3/5
Tell whether it is possible to draw a figure with the given description.
a triangle with sides of length 5 inches and 6 inches that meet at a 50° angle
Is it possible or not possible. Will give brinliest
Answer:
in my opinion it is not possibleStep-by-step explanation:
hope it helps you have a good day
NEED HELP ASAP PLEASE! BRAINLIEST TO RIGHT ANSWER! Are the polygons similar? If they are, write a similarity statement and give the scale factor.
Answer:
B) Yes; POSN~KDAG; scale factor 5:4
Step-by-step explanation:
B) Yes; POSN~KDAG; scale factor 5:4
Same angles (If 3 are the same, the 4th is the same).
Comparing the 4 respective sides:
15/12=5/4
10/8=5/4
7.5/6=5/4
15/12=5/4
A sample of bacteria is decaying according to the half-life model f(t) = Ne -0.226t, where N is the initial sample size and t
is time in hours. At t = 4, there are 25 bacteria remaining. What was the initial sample amount? Round your answer to the
nearest whole number, and do not include units.
Answer:
Step-by-step explanation:
A sample of bacteria is decaying according to the half-life model f(t) = Ne -0.226t, where N is the initial sample size and t
is time in hours. At t = 4, there are 25 bacteria remaining. What was the initial sample amount? Round your answer to the
nearest whole number, and do not include units.
A baker has small and large bags of sugar for making cakes. The large bag contains 30 cups cups of sugar and is 2.5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. How many cakes can be made with a large bag of sugar?
Answer:
Step-by-step explanation:
The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.
What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.
9x + 0.75 = 12
First, subtract 0.75 from both sides. With that, we can solve for x directly.
9x = 12 - 0.75
9x = 11.25
Now, divide both sides by 9.
x = 11.25/9
x = 1.25
With that, we now know that each cake needs 1.25 cups of sugar.
With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.
With that done, we have our answer. 24 cakes can be made with a large bag of sugar.
I hope this helps! (⌒ω⌒)
Find y.
1)6.76
2)7.54
3)18.55
4)29.83
9514 1404 393
Answer:
(c) 18.55
Step-by-step explanation:
The law of sines tells you ...
y/sin(106°) = 15/sin(51°)
y = 15×sin(106°)/sin(51°)
y ≈ 18.55
_____
The same kind of proportion can find x:
x = 15×sin(23°)/sin(51°)
x ≈ 7.54
Please note that the question posted here asks for the value of y. The value of x and the complete triangle solution are provided as a courtesy to those who may be asked for other values in this triangle.
If I apply distributive property to 6 (t + 12) = 114 then what operation will I need to use first
Answer:
Step-by-step explanation:
First divide 6 from the left size so it gets cancelled.
Basically 6 (t + 12) = 114 becomes (t + 12) = 114/6
Which becomes (t + 12) = 19
Now, (t + 12) - 12 = 19
Therefore, t = 19 - 12
Answer: t = 7
(whatever you do to one side, most be done to the other side too).
To check,
6(t+12)=114
6(7+12)=114
Solve brackets first, 6(19)=114
114=114
The first operation will be multiplying 6 with t and 6 with 12 and then adding both the terms also t is equal to 7.
What is Distributive property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
As per the given data:
To apply distributive property in 6 (t + 12) = 114
Distributive property: A (B + C) = A × B + A × C
Now for, 6 (t + 12) = 114
First operation will be multiplying 6 with t and 6 with 12 and then adding both the terms:
6 × t + 6 × 12 = 114
6t + 72 = 114
6t = 114 - 72
6t = 42
t = (42/6) = 7
Hence, the first operation will be multiplying 6 with t and 6 with 12 and then adding both the terms also t is equal to 7.
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Pick the correct value for the image of A after applying the rotation matrix.
(- 3, -4)
(- 1, -4)
(1, -4)
(3, -4)
Answer:
A) (- 3, -4)
Step-by-step explanation:
edge 2021
Answer:
A) (-3, -4)
Step-by-step explanation:
If ∠1 and ∠2 are vertical angles and m∠2 = 108°, find m∠1.
Answer:
angle 1 = 108°
Step-by-step explanation:
because angle 1 and angle 2 are vertical angles and vertical angles are equal.
In rectangle ABCD,If EC=13 find BD
Answer:
[tex]BD = 26\\[/tex]
Step-by-step explanation:
Given
[tex]EC = 13[/tex]
Required
Find [tex]BD[/tex]
In the given rectangle.
AC and BD are the diagonals.
This implies that:
[tex]AC = BD[/tex]
AC is calculated as:
[tex]AC = AE + EC[/tex]
Where
[tex]AE = EC[/tex]
So:
[tex]AC = EC + EC[/tex]
[tex]AC = 13+13[/tex]
[tex]AC = 26[/tex]
Recall that: [tex]AC = BD[/tex]
[tex]BD = 26\\[/tex]
Simplify 4x + 3x² + x² - 3x
Answer:
[tex]x + {4x}^{2} [/tex]
Step-by-step explanation:
simplify by combining like terms
4x - 3x = x
[tex]3x ^{2} + {x}^{2} = {4x}^{2} [/tex]
we're left with
[tex]x + {4x}^{2} [/tex]
Answer:
4x²+x
Step-by-step explanation:
4x-3x+3x²+x²
4x minus 3x is x and 3x² +x² is 4x²
therefore,
4x²+x
$410 is invested in an account earning 4.2% interest (APR), compound quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
How is the graph of the parent quadratic function transformed to produce the graph of y--(2x+6)2+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated
up 3 units
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated
up 3 units
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up
3 units
O The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up
3 units
Answer: a
Step-by-step explanation:
just took the test
What is the slope of the line that goes through (0,0) and (6, 3)?
Answer:
0.5
Step-by-step explanation:
so the slope is also known as the gradient in y=mx+c
The mean number of points in 1977 was 1189 points with standard deviation of 397 points. With a roughly normal distribution, what percent of performances would fall between 395 and 1983 points?
Your answer
A. 100%
B. 68%
C. 95%
D.99.7%
Answer:
C. 95%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1189 points, standard deviation of 397 points.
Percentage between 395 and 1983 points?
395 = 1189 - 2*397
1983 = 1189 + 2*397
So within 2 standard deviations of the mean, which by the Empirical Rule is approximately 95%, and the answer is option C.
PLEASE HELP!
I AM IN A HURRY
Answer:
Honestly I have no idea what is going on in this passage or whatever it is.
Step-by-step explanation:
Solve for x.
5(x + 1) = 4(X + 8)
Ox= 37
Ox=7
Ox=27
Ox=17
Help please
Answer:
27
Step-by-step explanation:
What formula can be used to find circumference? Choose all that apply. *
Cat
2r
nd
2nd
Answer:
circumference =pi ×diameter
OR
pi × radius × 2
find the highest common factor of 12,20 and 28
no links
Answer:
the highest or greatest common factor 12,20,and 28 is 4
Answer:
12, 20, 28.
Step-by-step explanation:
here is the answer
no links
no photos
just a simple answer
have a great day/night
:)
i will be sooooo thankful if u helped me
Answer:
For 35 its C
Step-by-step explanation:
Please help me with this ASAP ASAP please please help
Answer:
Step-by-step explanation:
Base perimeter: 4 x 2 x π = 8π
LA = 8π x 6 = 48π
Base area = 4^2π = 16π
SA = 16π x 2 + 48π = 80π
V= 16π x 6 = 96π
What is the mean for these numbers?
5,5,5,5
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT'S A COMPUTER PHONE AND TABLET VIRUS
Answer:
5
Step-by-step explanation:
Complete the square
to find the vertex
of this parabola.
y^2+4x - 2y+21=0
Answer:
::::::::::::::::::::
(-5,1)
The vertex of the parabola represented by the equation y² + 4x - 2y + 21 = 0 is (-5, 1).
The parabola is represented by the equation y² + 4x - 2y + 21 = 0.
Take the coefficient of y, which is -2, divide it by 2, and square the result:
(-2/2)² = 1
Now, we add and subtract this value inside the parentheses to maintain the equation's balance:
y² - 2y + 1 + 4x + 21 - 1 = 0
Rearranging the terms, we have:
(y² - 2y + 1) + 4x + 20 = 0
Now, the terms inside the parentheses can be written as a perfect square:
(y - 1)² + 4x + 20 = 0
Setting (y - 1)² = 0,
(y - 1)² = 0
y - 1 = 0
y = 1
Substitute y = 1 back into the equation to find the x-coordinate of the vertex:
(1 - 1)² + 4x + 20 = 0
0 + 4x + 20 = 0
4x = -20
x = -5
Therefore, the vertex of the parabola is (-5, 1).
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Solve 3y^3 + 12y^2 + 12y =0
Please
Answer:
y = 0, -2
Step-by-step explanation:
Factor out the common term 3y.
[tex]3y( {y}^{2} + 4y + 4) = 0[/tex]
Rewrite y² + 4y + 4 in the form of a² + 2ab + b², where a = y and b = 2.
[tex]3y( {y}^{2} + 2(y)(2) + {2}^{2} ) = 0[/tex]
Use square sum: (a + b)² = a² + 2ab + b².
[tex]3y(y + 2) ^{2} = 0[/tex]
solve for y.
y = 0, -2.
therefor, the answer for this equation is 0, - 2.
What fraction is equivalent to 10 and has a denominator of 100? (2 points)
6
100
7
60
100
o
600
100
a
60
10
Answer:
1000 / 100
Step-by-step explanation:
Answer:
ff
Step-by-step explanation:
Elijah bought a new car for $25,000. He paid
$5,000 up front and then $600 per month. How
many months will it take Elijah to pay off the car?
Answer: 6 days too be exact
Step-by-step explanation:
Answer:
33.333 months
Step-by-step explanation:
25,000-5,000=20,000
20,000/600=33.333
If he payed $5,000 upfront, the he only has $20,000 remaining to pay. If he is paying $600 a month then you divide the $20,000 by the $600 to 33.333 months. Hope this helps
simplify 8x+7-x-4
help meeeeee!!!
Answer:
7x + 3
Step-by-step explanation:
Let's simplify step-by-step.
8x + 7 − x − 4
= 8x + 7 + −x + −4
Combine Like Terms:
= 8x + 7 + −x + −4
= (8x + −x) + (7 + −4)
= 7x + 3
Answer:
= 7x + 3
hope this helps and is right. p.s i really need brainliest :)
if my answer is wrong then I am incredibly sorry!
A baker uses 5 cups of flour to make 75 cookies. Using this same ratio, how many cups of flour will be needed for 45 cookies? Use the ratio table given to solve the problem.
Answer:
Since, the baker use 5cups for 75cookies.Then for 30 cookies number of cups=
=75/5
=15.
Therefore no. 1cups for 15cookies.so,for 30 cookies=
=15*2
=30.
So, 2cups are needed for 30cookies
If x is an acute angle, and tan x=3/4
evaluate
COS x-sin x/COS x+ sin x
please answer fast 10 points and brainliest answer
Use the pic and solve the COS x-sin x/COS x+ sin x part
comment if there's something u don't understand
The value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
tanx = 3/4 (x is an acute angle)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}-1=\dfrac{4}{3}-1\\\\\rm \dfrac{cosx-sinx}{sinx}=\dfrac{1}{3}\\\\[/tex] ….(1)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}+1=\dfrac{4}{3}+1\\\\\rm \dfrac{cosx+sinx}{sinx}=\dfrac{7}{3}\\\\[/tex] …(2)
Divide (1) ÷ (2)
(cosx-sinx)/(cosx+sinx) = (1/3)/(7/3) = 1/7
Thus, the value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
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Which shape is the base of the pyramid shown below?
A triangle
B square
Answer:
B. it's a square pyramid so the base is a square.
Step-by-step explanation: