Answer:
k=20t/a
Step-by-step explanation:
20t=ak
20t/a=k
k=20t/a
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
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!!!
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]
The point (5,-12) lies on the terminal side of an angel theta in standard position. Find the exact value of cot theta. Express the answer as a fraction reduced to the lowest term
Answer:
[tex]cot\theta=-\frac{5}{12}[/tex]
Step-by-step explanation:
We are given that the point (5,-12) lies on the terminal side of an angle theta in standard position.
We have to find the exact value of [tex]cot\theta[/tex].
Let
Point (x,y)=(5,-12)
[tex]r=\sqrt{x^2+y^2}[/tex]
Substitute the values
[tex]r=\sqrt{5^2+(-12)^2}[/tex]
[tex]r=\sqrt{169}=13[/tex]
We know that
[tex]cot\theta=\frac{x}{y}[/tex]
Using values
[tex]cot\theta=-\frac{5}{12}[/tex]
Complete the equation for the relationship between the weight and number of months
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
Please help me on this question
Answer:
√20
Or
2√5
Step-by-step explanation:
It is very easy just substitute
It will be:
4 1/3 - 2 1/2 divided by 1 2/3
Answer:
Exact Form: [tex]\frac{17}{6}[/tex]
Decimal Form: 2.83
Mixed Number Form: [tex]2 and 5/6[/tex]
Step-by-step explanation:
Answer:
[tex]1\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]4\frac{1}{3}-2\frac{1}{2}[/tex]
[tex]4\frac{2}{6} -2\frac{3}{6}=1\frac{5}{6}[/tex]
[tex]1\frac{5}{6} =\frac{11}{6}[/tex]
[tex]1\frac{2}{3}=\frac{5}{3}[/tex]
[tex]\frac{11}{6}[/tex] ÷ [tex]\frac{5}{3} =[/tex]
[tex]\frac{11}{6} *\frac{3}{5}=[/tex]
[tex]\frac{11}{2}*\frac{1}{5} =[/tex]
[tex]=\frac{11}{10}[/tex]
[tex]=1\frac{1}{10}[/tex]
Hope this is helpful
write tge following numbers expanded forms.
23900068407
Answer:
Step-by-step explanation:
20000000000+3000000000+900000000+60000+8000+400+7
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
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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Help please guys if you don’t mind
Answer:
first
2/5m + 8/5
second
22/5
third
11
Put these numbers in order from least to greatest.
9.9, 9.5, and 9 4/5
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]
2 Points
(25x
0
The equation ya
represents Michelle's regular
130(x-38) +950 %> 38
hourly and overtime wage. Based on this equation, what is Michelle's
overtime hourly pay?
A. $30
B. $38
O C. $950
O D. $25
Answer:
The answer is "35.22".
Step-by-step explanation:
Let the given equation:
[tex]\to 130(x-38) +950 \% \times 38=0\\\\\to 130x- 4940+\frac{950}{100} \times 38=0\\\\\to 130x- 4940+9.5\times 38=0\\\\\to 130x- 4940+361=0\\\\\to 130x- 4579=0\\\\\to 130x= 4579\\\\\to x= \frac{4579}{130}\\\\\to x= 35.22[/tex]
Answer: $25
Step-by-step explanation: took the quiz
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
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
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
Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in josiahs account, y, after x years?
a-y=360(1.3)^x
b-y=360(0.3^x
c-y=360(0.03)^x
d-y=360(1.03)^x
Answer:
y = 360 (1.03)^x
Step-by-step explanation:
Amount in account = principle * (1+ rate) ^ time
When the interest is annual
rate is in decimal form and time is in years
y = 360 ( 1+.03) ^x
y = 360 (1.03)^x
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
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.
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
Consider y=h(θ) described in the table. When comparing h(θ) to the parent function f(θ)=cos(θ), which statements are true? Select all that apply.
2 Answers:
Choice AChoice E=====================================================
Explanation:
Let's go through the answer choices
---------------------------------
A)
The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.
The midline of [tex]h(\theta)[/tex] is y = 14.
Consider that the parent function [tex]\cos(\theta)[/tex] has a midline of y = 0. The jump from y = 0 to y = 14 must mean [tex]h(\theta)[/tex] has a vertical shift of 14.
Choice A is true
---------------------------------
B)
The period is the length of the cycle. For the function [tex]h(\theta)[/tex], the function starts at [tex]\theta = 0[/tex] and repeats when it gets to [tex]\theta = \frac{\pi}{2}[/tex]. This is a difference of pi/2 units which is the period.
Choice B is false. It contradicts with choice E.
---------------------------------
C)
Choice C is false. The max for [tex]h(\theta)[/tex] is at y = 27
---------------------------------
D)
To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.
Or we can note the distance from the midline to the min is 14-1 = 13 units.
Or we subtract the min and max, and divide by 2: (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13
Either way, the amplitude is 13 units
Choice D is false.
---------------------------------
E)
Choice E is true. Refer to choice B to see why this is the case.
---------------------------------
Side note: one possible function is [tex]h(\theta) = 13\cos(4\theta+\pi) + 14[/tex]. The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.
The correct two options are h(Ф) has vertical shift of 14 and Choice E
The period of a fuction is x/2
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Let's go through the answer choices
A)
The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.
The midline of is y = 14.
Consider that the parent function has a midline of y = 0. The jump from y = 0 to y = 14 must mean has a vertical shift of 14.
Choice A is true
B)
The period is the length of the cycle. For the function , the function starts at and repeats when it gets to . This is a difference of pi/2 units which is the period.
Choice B is false. It contradicts with choice E.
C)
Choice C is false. The max for is at y = 27
D)
To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.
Or we can note the distance from the midline to the min is 14-1 = 13 units.
Or we subtract the min and max, and divide by 2: (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13
Either way, the amplitude is 13 units
Choice D is false.
E)
Choice E is true. Refer to choice B to see why this is the case.
Side note: one possible function is h(Ф) = 13 Cos(4Ф + π) + 14 . The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.
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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
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]
Find an equation for the perpendicular bisector of the line segment whose endpoints are (8,-5)(8,−5) and (4,3)(4,3).
Answer:
[tex]Correct answer\\y=\frac{1}{2} x-4[/tex]
Step-by-step explanation:
[tex]y-\frac{-5+3}{2} =\frac{-1}{\frac{3-(-5)}{4-8} } (x-\frac{4+8}{2} )\\y+1=\frac{1}{2} (x-6)\\y=\frac{1}{2} x-4[/tex]
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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Helppp and explain pleaseeeeee!!!!!!
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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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