Answer:
1/6 + 1/2 = 1/6 + 3/6 = 4/6
SIMPLIFIED IS = 2/3
Step-by-step explanation:
Mrs Martin has $7000 in her saving account. Alonzo has 1/10 as much money in his account as Mrs Martin. How much money does Alonzo have in his account?
Answer:
7000*1/10
In a calculator type in 7000*(1/10)
700
Step-by-step explanation:
Find the inverse of f(x) = -4+7/2x
Answer:
2/7x + 8/7
Step-by-step explanation:
f(x) = -4 + 7/2x
y = -4+7/2x
Exchange x and y
x = -4 +7/2y
Solve for y
Add 4 to each side
x+4 = -4+4 +7/2y
x+4 = 7/2y
Multiply each side by 2/7
2/7(x+4) = 2/7 * 7/2y
2/7(x+4) = y
2/7x + 8/7
Can anyone plzz tell me the reasons for this false ones
Plzz help
Answer:
It is correct
Step-by-step explanation:
Has two solutions x = a and x = -a because both numbers are at the distance a from 0. You begin by making it into two separate equations and then solving them separately. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
let f(x)=2x-1 and g(x)=1/x. Find the value of f(g(7))
Answer:
-5/7
Step-by-step explanation:
We need to find g(7) first
All we have to is plug 7 in the place of x
g(7) = 1/7
Now we have f(1/7) = 2x - 1
f(1/7) = 2(1/7) - 1
f(1/7) = 2/7 - 1
Don't forget about common denominators
2/7 - 7/7 = -5/7
A bacteria culture doubles every 5 hours. Determine the hourly growth rate of the bacteria
culture. Round your answer to the nearest tenth of a percent.
Answer:
10
Step-by-step explanation:
Using an exponential function, it is found that the hourly growth rate of the bacteria culture is of 14.9%.
------------------------
An exponential function has the following format:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which:
A(0) is the initial amount.r is the hourly growth rate.------------------------
Since it doubles every 5 hours, it means that:
[tex]A(5) = 2A(0)[/tex]
And we use this to find r.
------------------------
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]2A(0) = A(0)(1+r)^5[/tex]
[tex](1 + r)^5 = 2[/tex]
[tex]\sqrt[5]{(1 + r)^5} = \sqrt[5]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.149[/tex]
[tex]r = 1.149 - 1 = 0.149[/tex]
0.149*100% = 14.9%.
The hourly growth rate of the bacteria culture is of 14.9%.
A similar problem is given at https://brainly.com/question/24218305
PMDAS
1. 24 + 8 + (9 x2) x 4 + 7
Answer:
[tex]\huge\boxed{\sf 111}[/tex]
Step-by-step explanation:
= 24 + 8 + (9 x 2) x 4 + 7
Parenthesis
= 24 + 8 + 18 x 4 + 7
Multiplication
= 24 + 8 + 72 + 7
Addition
= 32 + 72 + 7
= 104 + 7
= 111
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden?
Do not include units in your answer.
Given : The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden ?
Solution :
Let us assume the breadth be x
The length is 4 ft longer than the Breadth
So, the length be x + 4
Perimeter = 192
❍ Perimeter = 2(Length + Breadth)
192 = 2(x + 4 + x) 192 = 2(2x + 4) 192 = 4x + 8 192 - 8 = 4x 4x = 184 x = 46Length : x + 4 = 46 + 4 = 50
Breadth : x = 46
If I'm 4years and my brother is half of my age now I'm 44 how old is he ?
Answer:
42 years
Step-by-step explanation:
if u were 4 years then your brother will be 2 years
if u r 44 then u can see that the difference between your previous age aand your brothers was 2 years
so here u just need to substract 2
44- 2 that will be 42
Solve for n.
n + 1 = 4(n-8)
0 n = 1
0 n = 8
0 n = 11
0 n = 16
n + 1 = 4(n - 8)
n + 1 = 4n - 32
n - 4n = -32 - 1
-3n = -33 / : (-3)
n = 11
Please help me to solve this question
Answer:
(p+5)(p-2)
Step-by-step explanation:
We are looking for two numbers that multiply to -10 (the rightmost number) and sum to 3 (the middle number)
These are 5 and -2
So we write
(p ____)(p ____)
and fill in the blanks
(p+5)(p-2)
Check by FOILing:
p^2 -2p + 5p -10
And combine the two middle terms.
p^2 + 3p - 10
14 - 2(x + 8) = 5x - (3x - 34); Prove: x = -9
Step-by-step explanation:
14 - 2(x + 8) = 5x - (3x - 34)
14 -2x -16 = 5x -3x+34
-2x -2 = 2x+34
-2x-2x = 34+2
-4x = 36
x = 36/(-4)
x = -9
Find the equation of the line that is parallel to y = 4 - 3x and passes through the
point (1,5).
Answer:
[tex]y=-3x+8[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope1) Determine the slope (m)
[tex]y = 4 - 3x\\y = -3x+4[/tex]
Given this equation, we can identify the slope to be -3 since it's in the place of m in [tex]y=mx+b[/tex].
Because parallel lines have the same slope, -3 is therefore the slope of the line we're currently solving for. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-3x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-3x+b[/tex]
Plug in the given point (1,5) and solve for b:
[tex]5=-3(1)+b\\5=-3+b\\8=b[/tex]
Therefore, the y-intercept is 8. Plug this back into [tex]y=-3x+b[/tex]:
[tex]y=-3x+8[/tex]
I hope this helps!
I'LL GIVE BRAINLIEST;
You deposit $400 each month into an account earning 5% annual interest compounded monthly.
a) How much will you have in the account in 20 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
Answer:
amount in 30 yrs is: $1787.0977
interest is for 20 yrs: $1387.0977
Step-by-step explanation:
Given data
principal amount = $400
rate = 5 % = 0.05
time period = 20 years
(Sorry if I'm wrong :( )
The diameter of a quarter is 0.955 inches. If you laid 1,000,000 quarters side to
side, how far would that be?
Examine the tile pattern at right
b. The pattern grow by adding 1 tile above the tile and adding 1 tile at the right of the tile.
c. In figure 0, there will be 1 tile. We know this because in each successive figures a tile is added at the above and a tile is added to the right, so ineach preceeding figure the same is reduced. In figure 1, there are e tiles, so in figure 0, there will be 3-2 = 1 tile.
A spelunkers starts his journey at -500 feet and ends up at -100 feet.What is his change in elevation?
Answer:
+400
Step-by-step explanation:
What is p (salamander)?
Answer:
the image/question isnt there
Step-by-step explanation:
Answer:
Step-by-step explanation:
m={y:y is a multiple of 3,5<y<10}
Answer:
6,9
Step-by-step explanation:
The two multiples of 3
which are more than 5 and less than 10 are
6 and 9
Multiply:
(2sin B+cos B)by 3cosec B.secB
Step-by-step explanation:
Is this the full question
Let z=3+i,
then find
a. Z²
b. |Z|
c.[tex]\sqrt{Z}[/tex]
d. Polar form of z
Given z = 3 + i, right away we can find
(a) square
z ² = (3 + i )² = 3² + 6i + i ² = 9 + 6i - 1 = 8 + 6i
(b) modulus
|z| = √(3² + 1²) = √(9 + 1) = √10
(d) polar form
First find the argument:
arg(z) = arctan(1/3)
Then
z = |z| exp(i arg(z))
z = √10 exp(i arctan(1/3))
or
z = √10 (cos(arctan(1/3)) + i sin(arctan(1/3))
(c) square root
Any complex number has 2 square roots. Using the polar form from part (d), we have
√z = √(√10) exp(i arctan(1/3) / 2)
and
√z = √(√10) exp(i (arctan(1/3) + 2π) / 2)
Then in standard rectangular form, we have
[tex]\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)[/tex]
and
[tex]\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)[/tex]
We can simplify this further. We know that z lies in the first quadrant, so
0 < arg(z) = arctan(1/3) < π/2
which means
0 < 1/2 arctan(1/3) < π/4
Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have
[tex]\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}[/tex]
[tex]\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}[/tex]
and since cos(x + π) = -cos(x) and sin(x + π) = -sin(x),
[tex]\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}[/tex]
[tex]\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}[/tex]
Now, arctan(1/3) is an angle y such that tan(y) = 1/3. In a right triangle satisfying this relation, we would see that cos(y) = 3/√10 and sin(y) = 1/√10. Then
[tex]\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}[/tex]
[tex]\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}[/tex]
[tex]\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}[/tex]
[tex]\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}[/tex]
So the two square roots of z are
[tex]\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}[/tex]
and
[tex]\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}[/tex]
Answer:
[tex]\displaystyle \text{a. }8+6i\\\\\text{b. }\sqrt{10}\\\\\text{c. }\\\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}+i\sqrt{\frac{\sqrt{10}-3}{2}},\\-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}-i\sqrt{\frac{\sqrt{10}-3}{2}}\\\\\\\text{d. }\\\text{Exact: }z=\sqrt{10}\left(\cos\left(\arctan\left(\frac{1}{3}\right)\right), i\sin\left(\arctan\left(\frac{1}{3}\right)\right)\right),\\\text{Approximated: }z=3.16(\cos(18.4^{\circ}),i\sin(18.4^{\circ}))[/tex]
Step-by-step explanation:
Recall that [tex]i=\sqrt{-1}[/tex]
Part A:
We are just squaring a binomial, so the FOIL method works great. Also, recall that [tex](a+b)^2=a^2+2ab+b^2[/tex].
[tex]z^2=(3+i)^2,\\z^2=3^2+2(3i)+i^2,\\z^2=9+6i-1,\\z^2=\boxed{8+6i}[/tex]
Part B:
The magnitude, or modulus, of some complex number [tex]a+bi[/tex] is given by [tex]\sqrt{a^2+b^2}[/tex].
In [tex]3+i[/tex], assign values:
[tex]a=3[/tex] [tex]b=1[/tex][tex]|z|=\sqrt{3^2+1^2},\\|z|=\sqrt{9+1},\\|z|=\sqrt{10}[/tex]
Part C:
In Part A, notice that when we square a complex number in the form [tex]a+bi[/tex], our answer is still a complex number in the form
We have:
[tex](c+di)^2=a+bi[/tex]
Expanding, we get:
[tex]c^2+2cdi+(di)^2=a+bi,\\c^2+2cdi+d^2(-1)=a+bi,\\c^2-d^2+2cdi=a+bi[/tex]
This is still in the exact same form as [tex]a+bi[/tex] where:
[tex]c^2-d^2[/tex] corresponds with [tex]a[/tex] [tex]2cd[/tex] corresponds with [tex]b[/tex]Thus, we have the following system of equations:
[tex]\begin{cases}c^2-d^2=3,\\2cd=1\end{cases}[/tex]
Divide the second equation by [tex]2d[/tex] to isolate [tex]c[/tex]:
[tex]2cd=1,\\\frac{2cd}{2d}=\frac{1}{2d},\\c=\frac{1}{2d}[/tex]
Substitute this into the first equation:
[tex]\left(\frac{1}{2d}\right)^2-d^2=3,\\\frac{1}{4d^2}-d^2=3,\\1-4d^4=12d^2,\\-4d^4-12d^2+1=0[/tex]
This is a quadratic disguise, let [tex]u=d^2[/tex] and solve like a normal quadratic.
Solving yields:
[tex]d=\pm i \sqrt{\frac{3+\sqrt{10}}{2}},\\d=\pm \sqrt{\frac{{\sqrt{10}-3}}{2}}[/tex]
We stipulate [tex]d\in \mathbb{R}[/tex] and therefore [tex]d=\pm i \sqrt{\frac{3+\sqrt{10}}{2}}[/tex] is extraneous.
Thus, we have the following cases:
[tex]\begin{cases}c^2-\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\\c^2-\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\end{cases}\\[/tex]
Notice that [tex]\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2[/tex]. However, since [tex]2cd=1[/tex], two solutions will be extraneous and we will have only two roots.
Solving, we have:
[tex]\begin{cases}c^2-\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3 \\c^2-\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\end{cases}\\\\c^2-\sqrt{\frac{5}{2}}+\frac{3}{2}=3,\\c=\pm \sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}[/tex]
Given the conditions [tex]c\in \mathbb{R}, d\in \mathbb{R}, 2cd=1[/tex], the solutions to this system of equations are:
[tex]\left(\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}, \sqrt{\frac{\sqrt{10}-3}{2}}\right),\\\left(-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}},- \frac{\sqrt{10}-3}{2}}\right)[/tex]
Therefore, the square roots of [tex]z=3+i[/tex] are:
[tex]\sqrt{z}=\boxed{\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}+i\sqrt{\frac{\sqrt{10}-3}{2}} },\\\sqrt{z}=\boxed{-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}-i\sqrt{\frac{\sqrt{10}-3}{2}}}[/tex]
Part D:
The polar form of some complex number [tex]a+bi[/tex] is given by [tex]z=r(\cos \theta+\sin \theta)i[/tex], where [tex]r[/tex] is the modulus of the complex number (as we found in Part B), and [tex]\theta=\arctan(\frac{b}{a})[/tex] (derive from right triangle in a complex plane).
We already found the value of the modulus/magnitude in Part B to be [tex]r=\sqrt{10}[/tex].
The angular polar coordinate [tex]\theta[/tex] is given by [tex]\theta=\arctan(\frac{b}{a})[/tex] and thus is:
[tex]\theta=\arctan(\frac{1}{3}),\\\theta=18.43494882\approx 18.4^{\circ}[/tex]
Therefore, the polar form of [tex]z[/tex] is:
[tex]\displaystyle \text{Exact: }z=\sqrt{10}\left(\cos\left(\arctan\left(\frac{1}{3}\right)\right), i\sin\left(\arctan\left(\frac{1}{3}\right)\right)\right),\\\text{Approximated: }z=3.16(\cos(18.4^{\circ}),i\sin(18.4^{\circ}))[/tex]
18. Solve x^2+ 6x - 16 = 0 by completing the square.
Please give detailed steps!!
Answer:
x1 = -8, x2= 2
Step-by-step explanation:
1. Write 6x as a difference
= x^2 + 8x - 2x - 16 = 0
2. Factor the expressions
= x ( x + 8 ) - 2x - 16 = 0
= x ( x + 8 ) - 2 ( x + 8 ) = 0
Factor out x + 8 from the expression
= ( x + 8 ) ( x - 2 ) = 0
3. When the product of factors = 0, at least one factor is 0
x + 8 = 0
x - 2 = 0
4. Solve the equation for x
x = - 8
x = 2
Therefore, the equation has 2 solutions :
x1 = -8, x2 = 2
Help me with math really quickly It costs $20 plus $1.50 per hour to rent a golf cart. a. Write an equation that shows the relationship between the cost of renting a golf cart (y) and
the number of hours it was rented (x). b. Graph your equation. Be sure to label your axis and chose an appropriate scale. c. How much does it cost to rent a cart for 5 hours? d. How many hours can you rent a cart for $32?
Answer:
a) 1.50x + 20 = y
c) $27.5
d) 8 hours
Step-by-step explanation:
a) 1.50 times x the amount of hours. 1.50 per hour. 1 hour would be 1.50 and 2 hours would be 3.00. Then just add 20 to that amount.
b) Don't really have time to graph, but here this is the graph using a graphing calculator. It intercepts at 20 because 20 is b, which is the y intercept.
c) Plug in 5 for x
d) Start with 1.50x + 20 = 32. You need to solve for x. Subtract 20 from both sides and you get 1.50x = 12. Divide both sides by 1.50 and you get x = 8. Since x representshe amount of hours, it would be x.
What is 1^2 + 0.1^2?
Answer:
1.01
Step-by-step explanation:
1^2= 1
0.1^2= 0.01
1+0.01=1.01
5 men can paint 2 identical houses in 3 days. Assuming
that all the men work at the same rate, how long
will it take 10 men to paint 8 such houses?
Plz help I’ll mark brainliest
Answer:
6 days
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:6 days
Step-by-step explanation:
because it means 5 men painted 1 house in 1.5days(3:2=1,5), so for 5 men to paint 8 houses they will need 12 days (1.5x8=12) divide 12 in half because there will be twice as much men(10) and you get 6 days
The average number of road accidents that occur on a particular stretch of road during a month is 7. What is the probability of observing exactly three accidents on this stretch of road next month
Answer:
3/7 or 57.1%
Step-by-step explanation:
If the car wrecks happen 7 times a month and you see 3 wrecks, then you would have seen 3 out of the 7 wrecks. 3/7 or 57.1% of wrecks.
The required probability of observing exactly three accidents is 42.8%.
Give that,
The average number of road accidents that occur on a particular stretch of road during a month is 7. What is the probability of observing exactly three accidents on this stretch of road next month is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Total number of samples = 7
Total number of favorable outcomes = 3
Required probability = 3 / 7 = 42.8%
Thus, the required probability of observing exactly three accidents is 42.8%.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
In a group 40% like football ,70% like cricket and 30% like both games
Step-by-step explanation:
Ans is 20 .
F union C whole complement is 20
2.53 x 0.0041
(please help)
Answer:
0.010373
Step-by-step explanation:
hope it helps!
Which fraction is equivalent to -7/8
1. 8/-7
2. -7/-8
3. 8/7
4. 7/-8
Answer:
Your answer is answer no 4 = 7/-8
Answer:
4.
Step-by-step explanation:
7/-8
-7/8 is between -1 and 0.
So, we can eliminate 1 and 3.
We can also get rid of 2 because -7/-8 = 7/8, which is positive.
We are left with 4.
HELPPPPPPPPPPPPPPPPPPPPP
Answer:
B
Step-by-step explanation:
i took quiz
Help!!!!will have brainley I need help pls!
Option A " how the temperature of a cup of coffee changes as time passes ".
Hope it helps you.