Answer:
The slope of the perpendicular line will 1/3.
Step-by-step explanation:
Help please guys if you don’t mind
Answer:
first
2/5m + 8/5
second
22/5
third
11
provide explanation too please !
a piano teacher teaches 8 lessons in 6 hours.
the lessons are all the same length.
how long is one lesson, in minutes?
1 hour is 60 minutes
6 hours x 60 = 360 total minutes
Divide total time by number of lessons:
360/8 = 45
Each lesson was 45 minutes
a box contains 6 dimes, 8 nickels, 12 pennies, and 3 quarters. what is the probability that a coin drawn at random is not a dime
Add all the coins to get total coins:
6 + 8 + 12 + 3 = 29 total coins
Subtract dimes to find total of the coins that are not dimes:
29 -6 = 23
Probability of not picking a dime is the number of coins that aren’t dimes over total coins:
23/29
Find the length of the missing
Answer:
12
Step-by-step explanation:
using pythagoras theorem
here 15 is hypotenuse since it is opposite 0f 90 degree
9 and x are the other smaller sides of a triangle
according to pythagoras thorem the sum of square of two smaller sides of a triangle is equal to the square of hypotenuse. So,
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 225 - 81
x^2 = 144
x = [tex]\sqrt{144[/tex]
x = 12
5. What is x in the diagram?
Answer:
B
Step-by-step explanation:
we rule out all other 3 by the simple fact that the side is 9
Jada asked some students at her school how many hours they spent watching television last week, to the nearest hour. Here are a box plot and a histogram for the data she collected.
If anyone trolls imma be very sad :(
Answer:
100
Step-by-step explanation:
Based on the histogram given :
The vertical axis gives the number of student in the school :
For the range :
0 - 5 = 40
5 - 10 = 30
10 - 15 = 20
15 - 20 = 5
20 - 25 = 3
25 - 30 = 2
Taking the sum :
(40 + 30 + 20 + 5 + 3 + 2) = 100
the length of a pond is 1700 CM breadth is 14m and height is 1000 CM if a point is half filled calculate the volume of a water in the pond
Answer:
1190 m^3
Step-by-step explanation:
l = 1700 cm = 17 m
b = 14 m
h = 1000 cm = 10 m
Total volume = l × b × h
= 17 × 14× 10
= 2380 m^3
since it is half filled ,
Volume is half , so,
volume of water in pond = 2380 ÷ 2
= 1190 m^3
Complete the equation for the relationship between the weight and number of months
WILL GIVE BRAINLIEST
Hannah and Han are each trying to solve the equation x² – 8x + 26 = 0. They know that
x = -1 are i& - i, but they are not sure how to use this information to solve for x in their
equation.
Part 1- Here is Hannah's work:
x? - 8x + 26 = 0
X? – 8x = -26
Show Hannah how
to finish her work using completing the square and complex numbers.
Part 2- Han decides to solve the equation using the quadratic
formula. Here is the beginning of his
work
-b+V62-4ac
-(-8)+7-8)2–401|(26)
Finish using the quadratic formula. Simplify the final answer as much as possible.
Part one:
[tex]x^2-8x=-26[/tex]
Rewrite in the form [tex](x+a)^{2} =b[/tex]
[tex]\left(x-4\right)^2=-10[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
Solve [tex]x-4=\sqrt{-10} : x=\sqrt{10} i+4[/tex]
Solve [tex]x-4=\sqrt{-10} : x=-\sqrt{10} i+4[/tex]
[tex]x=\sqrt{10}i+4,\:x=-\sqrt{10}i+4[/tex]
Part two:
[tex]x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}{2\cdot \:1}[/tex]
Simplify [tex]\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}: 2\sqrt{10} i[/tex]
[tex]=\frac{-\left(-8\right)\pm \:2\sqrt{10}i}{2\cdot \:1}[/tex]
Separate solutions
[tex]x_1=\frac{-\left(-8\right)+2\sqrt{10}i}{2\cdot \:1},\:x_2=\frac{-\left(-8\right)-2\sqrt{10}i}{2\cdot \:1}[/tex]
[tex]\frac{-(-8)+2\sqrt{10}i }{2*1} :4+\sqrt{10}i[/tex]
[tex]\frac{-(-8)+2\sqrt{10}i }{2*1} :4-\sqrt{10}i[/tex]
[tex]x=4+\sqrt{10}i,\:x=4-\sqrt{10}i[/tex]
The solutions are:-
[tex]x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is
[tex]x^2- 8x + 26 = 0\\\\x^2-8x=-26\\\\(x-4)^2=-10\\\\[/tex]
[tex](x-4)=[/tex]±[tex]\sqrt{-10}[/tex]
[tex]x=\sqrt{10}i+4\\\\x=-\sqrt{10}i+4[/tex]
So,
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\\\x=\frac{8+-\sqrt{(-8)^2-4(1)(26)}}{2(1)}\\\\x=\frac{8+-\sqrt{(-8)^2-4(1)(26)}}{2(1)}\\\\x=\frac{8+-\sqrt{64-104}}{2}\\\\x=\frac{8+-2\sqrt{10i}}{2}\\\\x=\frac{2(4+-\sqrt{10i})}{2}\\\\x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]
Hence, the solutions are:-
[tex]x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]
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the average length of string a and string d is 10x cm. the average length of string b and string c is 8x cm . the average length of strings b , c , d is 6x cm . find the length of string a in terms of x
Answer:
[tex]a = 18x[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}(a + d) = 10x[/tex]
[tex]\frac{1}{2}(b + c) = 8x[/tex]
[tex]\frac{1}{3}(b + c+d) = 6x[/tex]
Required
The value of (a)
We have:
[tex]\frac{1}{2}(a + d) = 10x[/tex] --- multiply by 2
[tex]\frac{1}{2}(b + c) = 8x[/tex] --- multiply by 2
[tex]\frac{1}{3}(b + c+d) = 6x[/tex] --- multiply by 3
So, we have:
[tex]\frac{1}{2}(a + d) = 10x[/tex]
[tex]a + d = 20x[/tex]
[tex]\frac{1}{2}(b + c) = 8x[/tex]
[tex]b + c = 16x[/tex]
[tex]\frac{1}{3}(b + c+d) = 6x[/tex]
[tex]b + c + d= 18x[/tex]
Substitute [tex]b + c = 16x[/tex] in [tex]b + c + d= 18x[/tex]
[tex]16x + d = 18x[/tex]
Solve for d
[tex]d = 18x - 16x[/tex]
[tex]d = 2x[/tex]
Substitute [tex]d = 2x[/tex] in [tex]a + d = 20x[/tex]
[tex]a + 2x = 20x[/tex]
Solve for (a)
[tex]a = 20x - 2x[/tex]
[tex]a = 18x[/tex]
How do I do this?? TnT
Answer:
x = 4
Step-by-step explanation:
Corresponding angles are congruent
4x + 44 = 6x + 36
44 = 2x + 36
8 = 2x
x = 4
Factorise a² - b²
.......
[tex]\longrightarrow{\green{ (a + b)(a - b) }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] ={a}^{2} - {b}^{2} [/tex]
[tex] = (a + b)(a - b)[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
wich is a solution to (x-3)(x+9)=-27?
Answer:
=0=−6
Step-by-step explanation:
Find the slope of the line that passes through (2 2) and (-1 -2)
Answer:
4/3
Step-by-step explanation:
The formula is (y1-y2) /(x1-x2)
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (- 1, - 2)
m = [tex]\frac{-2-2}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
Triangle HIJ is similar to triangle KLM. Find the measure of side MK. Round your answer to the nearest tenth.
Answer:
[tex]MK\approx 87.7[/tex]
Step-by-step explanation:
By definition, similar polygons have corresponding sides in a constant proportion. Therefore, we can set up the following proportion (ratio of corresponding sides) to solve for [tex]MK[/tex]:
[tex]\frac{20}{13}=\frac{MK}{57},\\MK=\frac{57\cdot 20}{13}\approx \boxed{87.7}[/tex]
Answer:
87.7
Step-by-step explanation:
Like stated previously similar triangle have side lengths with common ratios
*Create a proportionality to solve for MK*
57/13 = MK / 20
Now solve for MK
Multiply each side by 20
57/13 * 20 = 87.7 ( rounded )
MK/20 * 20 = MK
We're left with MK = 87.7
Helppp and explain pleaseeeeee!!!!!!
Can someone help me?It's urgent and thank you!
Answer:
y = square root x2 - 5
Step-by-step explanation:
y=[tex]\sqrt{x} -5[/tex]
(the top option)
Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated a constant rate per year. The table shows the value of the real estate after the first and second years:
Year:
1
2
Value (in dollars):
$200,038.80
$208,040.35
Which function best represents the value of the real estate after t years?
A. f(t) = 200,038.80(1.04)^t
B. f(t) = 200,038.80(0.04)^t
C. f(t) = 192,345(0.04)^t
D. f(t) = 192,345(1.04)^t
Answer:
D. f(t) = 192,345(1.04)^t
Step-by-step explanation:
I took the test and it was right.
Also that is the original price and when you look at exponential functions, the starting point or original price is always first the then rate of increase. The table just shows how it increased in year 1 and 2.
Hope this helps. :)
A function assigns the values. The function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The initial cost of industrial real estate is $192,345, while the cost after one year is $200,038.80. Therefore, the rate of appreciation is,
[tex]\$200,038.80 = \$192,345(1+R)^t\\\\\$200,038.80 = \$192,345(1+R)^1\\\\\dfrac{\$200,038.80}{\$192,345}=(1+R)^t\\\\1.04 = 1 + R\\\\R = 0.04[/tex]
Hence, the function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.
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explain by step by step pls :( if u type something wrong ill report u
Answer:
∠ C = ∠BCD = 30°
Step-by-step explanation:
∠ EDF = ∠GFC = 110° [ corresponding angles ]
Now consider triangle BCF
∠FBC + ∠ABC = 180° [ straight line angle ]
∠FBC + 100° = 180°
∠FBC = 180 - 100 = 80°
∠BFC + ∠GFC = 180° [ straight line angle ]
∠BFC + 110° = 180°
∠BFC = 180 - 110 = 70°
Sum of angles of triangle is 180°
Therefore , in triangle BCF
That is ,
∠F + ∠B + ∠ C = 180°
70° + 80° + ∠C = 180°
∠C = 180 - 150 = 30°
A scale model of a sculpture has a scale of 2:53
The height of the model is 20cm.
Find the height of the actual sculpture.
Give your answer in m.
Answer:
ok so we can simpley this is 1:106
so we multiply
20*106=2120 this is cm so we make it meters...
21.2meters!!!
Hope This Helps!!!
A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream in 180 minutes. Determine the steamer's speed in still water and the stream's speed.
Answer:
The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Step-by-step explanation:
Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.
Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').
he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')
The total time is thus t + t' = 36/(v + v') + 32/(v - v')
Since the whole trip takes 6,5 hours,
36/(v + v') + 32/(v - v') = 6.5 (1)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v') (1)
(v - v')36 + (v + v')32 = 6.5(v + v')(v - v') (1)
36v - 36v' + 32v + 32v' = 6.5(v² + v'²)
68v - 4v' = 6.5(v² + v'²) (2)
Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').
he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')
The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')
Since the whole trip takes 180 minutes = 3 hours,
4/(v + v') + 40/(v - v') = 3 (3)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v') (1)
(v - v')4 + (v + v')40 = 3(v + v')(v - v') (1)
4v - 4v' + 40v + 40v' = 3(v² + v'²)
44v - 36v' = 3(v² + v'²) (4)
Dividing (2) by (4), we have
(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)
(68v - 4v')/(44v - 36v') = 6.5/3
3(68v - 4v') = 6.5(44v - 36v')
204v - 12v' = 286v - 234v'
204v - 286v = 12v' - 234v'
-82v = -222v'
v = -222v'/82
v = 111v'/41
Substituting v into (2), we have
68v - 4v' = 6.5(v² + v'²)
68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²
[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²
[7384/41]v' = 6.5[14002/1681]v'²
[7384/41]v' = [91013/1681]v'²
[91013/1681]v'² - [7384/41]v' = 0
([91013/1681]v' - [7384/41])v' = 0
⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or v' = 7384/41 × 16841/91013
⇒ v' = 0 or v' = 180.097 × 0.185
⇒ v' = 0 or v' = 33.33 km/h
Since v' ≠ 0, v' = 33.33 km/h
Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h
So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Given the interval 0<θ<π/2. Find the angle θ which is formed by the line y = -2x+4 and y = 3x-3
Show your work as well, thank you!
Answer:
[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]
Step-by-step explanation:
we want to find the acute angle θ (as θ is between (0,π/2)) formed by the line y=-2x+4 and y=3x-3 to do so we can consider the following formula:
[tex] \displaystyle\tan( \theta) = \bigg| \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | [/tex]
[tex] \rm \displaystyle \implies\theta = \arctan \left( \bigg | \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | \right)[/tex]
From the first equation we obtain that [tex]m_1[/tex] is -2 and from the second that [tex]m_2[/tex] is 3 therefore substitute:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 2) (3)} \bigg | \right)[/tex]
simplify multiplication:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 6)} \bigg | \right)[/tex]
simplify Parentheses:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 + 2 }{1 + ( - 6)} \bigg | \right)[/tex]
simplify addition:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 5 }{ - 5} \bigg | \right)[/tex]
simplify division:
[tex] \rm\displaystyle \theta = \arctan \left( | - 1| \right)[/tex]
calculate the absolute of -1:
[tex]\rm\displaystyle \theta = \arctan \left( 1\right)[/tex]
calculate the inverse function:
[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]
hence,
the angle θ which is formed by the line y = -2x+4 and y = 3x-3 is π/4
(for more info about the formula refer the attachment thank you!)
Consider two vector-valued functions,
[tex]\vec r(t) = \left\langle t, -2t+4\right\rangle \text{ and } \vec s(t) = \left\langle t, 3t-3\right\rangle[/tex]
Differentiate both to get the corresponding tangent/direction vectors:
[tex]\dfrac{\mathrm d\vec r(t)}{\mathrm dt} = \left\langle1,-2\right\rangle \text{ and } \dfrac{\mathrm d\vec s(t)}{\mathrm dt} = \left\langle1,3\right\rangle[/tex]
Recall the dot product identity: for two vectors [tex]\vec a[/tex] and [tex]\vec b[/tex], we have
[tex]\vec a \cdot \vec b = \|\vec a\| \|\vec b\| \cos(\theta)[/tex]
where [tex]\theta[/tex] is the angle between them.
We have
[tex]\langle1,-2\rangle \cdot \langle1,3\rangle = \|\langle1,-2\rangle\| \|\langle1,3\rangle\| \cos(\theta) \\\\ 1\times1 + (-2)\times3 = \sqrt{1^2 + (-2)^2} \times \sqrt{1^2+3^2} \cos(\theta) \\\\ \cos(\theta) = \dfrac{-5}{\sqrt5\times\sqrt{10}} = -\dfrac1{\sqrt2} \\\\ \implies \theta = \cos^{-1}\left(-\dfrac1{\sqrt2}\right) = \dfrac{3\pi}4[/tex]
Then the acute angle between the lines is π/4.
Can someone tell me if this is the correct choice?
Answer:
Step-by-step explanation:
It's not the correct choice. If a root is given, that is the same thing as the solution. We go backwards from a solution to a factor, which is what you need to do here.
If x = 2i is the solution, then the factor is
(x - 2i). Likewise, with the other one.
If x = 3i is the solution, then the factor is
(x - 3i). The leading coefficient of 1 just sits outside the first set of parenthesis, and because multiplication is commutative, it doesn't matter which set you put first. Thus, the one you want looks like this:
f(x) = (x - 2i)(x - 3i) or
f(x) = (x - 3i)(x - 2i).
Put these numbers in order from least to greatest.
9.9, 9.5, and 9 4/5
Find two integers whose sum is 1 and product is -2
TWO INTERGES
Answer:
2 and -1
Step-by-step explanation:
sum = 2 + (-1)
= 1
product = 2 × ( -1)
= -2
Tell whether the equation Y=Y true or false
Answer:
its true trust biggie on this one fam
Step-by-step explanation:
its true broski
Which numbers are divisible by 2?
A)826
B)270
C)271
Answer:
A
Step-by-step explanation:
Answer:
A and B, every even number is divisible by two, C is odd
Al lanzar un dado dos veces consecutivas. ¿Qué probabilidad hay de obtener primero un 3 y luego un numero par?
Answer:
The probability is 1/12.
Step-by-step explanation:
Number of elements in sample space is 6 . Even numbers are 2, 4 and 6 so the there are 3 three even numbers.
So, the probability of getting 3 on the first chance and then an even number in the second chance is
[tex]P = \frac{1}{6}\times \frac{3}{6}\\\\P = \frac{1}{12}[/tex]
If R(x) = 2 – 3x – 1, find R(-2)
a. -3
b. 9
c. -9
d. -11
PLEASE HELP
Answer:
C
Step-by-step explanation:
C
The output of [tex]R(x) = x^{2} - 3x- 1[/tex] when x = -2 is 9.
What is PEMDAS?PEMDAS exists as an acronym for the terms parenthesis, exponents, multiplication, division, addition, and subtraction.
To estimate the value of R(-2)
Substitute the value of x = -2, then
[tex]R(-2) = (-2)^{2} - 3(-2) - 1[/tex]
By using the PEMDAS order of operations
Calculate exponents, [tex](-2)^2 = 4[/tex]
= 4 - 3(-2) - 1
Multiply and divide (left to right), 3(-2) = -6
= 4 - (-6) - 1
Add and subtract (left to right),
4 - (-6) - 1 = 9
Therefore, the value of R(-2) = 9.
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Kayleigh has $4500 in a savings account at the bank that earns 0.8% interest per year. How much
interest will she earn in 3 years?
Answer:
Kayleigh will have a total of $4608.
Step-by-step explanation:
First, you use the formula, I=PRT (Interest=Principal, Rate, Time), then you distribute the numbers: (I=4500x0.8%x3) when you multiply them all, you get $108, then you lastly add 108 to 4500, and you get your final answer of $4608.
Kayleigh will earn $108 in interest over a period of 3 years.
Interest is the additional amount of money that is charged or earned on a principal amount of money. It is typically expressed as a percentage of the principal and is either charged when borrowing money or earned when investing or saving money.
To calculate the interest Kayleigh will earn in 3 years, we can use the formula for simple interest:
Interest = Principal x Rate x Time
Given:
Principal = $4500
Rate = 0.8% = 0.008 (decimal form)
Time = 3 years
Plugging the values into the formula, we have:
Interest = $4500 x 0.008 x 3
Calculating the expression, we find:
Interest = $108
Therefore, Kayleigh will earn $108 in interest over a period of 3 years.
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