let m be the number of months. write an expression to show the total amount deposited after m months.​

Hello!

AC = AO + OC

The Pythagorean theorem!

AB² = BO² + AO²

AO² = AB² - BO²

AO² = 10² - 8²

AO² = 36

AO = √36

AO = 6

BC² = BO² + OC²

OC² = BC² - BO²

OC² = 17² - 8²

OC² = 225

OC = √225

OC = 15

So AC

= AO + OC

= 6 + 15

= 21

Answer:

AC = 21

Step-by-step explanation:

To find the length of AC, we have to first find the lengths of AO and OC and then add them together.

To find both the lengths of AO and OC, we have to use the Pythagorean theorem:

\(\boxed{a^2 + b^2 = c^2}\),

where:

c ⇒ length of the hypotenuse (longest side)

a, b ⇒ lengths of the two shorter sides

First, to find the length of AO, we can consider the triangle OAD. For this triangle, AD is the hypotenuse. Therefore,

AO² + OD² = AD²

⇒ AO² + 8² = 10²

⇒ AO² + 64 = 100

⇒ AO² = 100 - 64

⇒ AO² = 36

⇒ AO = √36

⇒ AO = 6

Next, to find the length of OC, we can consider the triangle OCD, whose hypotenuse is CD. Therefore,

OC² + OD² = CD²

⇒ OC² + 8² = 17²

⇒ OC² + 64 = 289

⇒ OC² = 289 - 64

⇒ OC² = 225

⇒ OC = √225

⇒ OC = 15

Now we can simply add the lengths of AO and OC to find the length of AC:

AC = AO + OC

⇒ AC = 6 + 15

⇒ AC = 21

Therefore, the length of AC is 21 units.

The equation of any straight line can be written as in slope intercept form as -

\(\green{ \underline { \boxed{ \sf{y=mx+c}}}} \)

where,

\(\begin{gathered}\begin{gathered}\\\implies\quad \sf y= 3x-9 \\\end{gathered} \end{gathered} \)

\(\longrightarrow\)Comparing the equation y = 3x -9 with the standard form of the equation, we get -

\(\quad \bull\: \sf m= 3\)

\(\quad \bull \: \sf c= -9\)

Thus, the line cross the y-axis at (0,-9) .

Answer: y=2x

Step-by-step explanation:

According to the given information, the value of the surface integral is 8/3.

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface integral of a vector field F over a surface S is given by:

∬S F ⋅ dS = ∬R (F ⋅ ru × rv) dA

where R is the parameter domain of the surface S, ru and rv are the partial derivatives of the position vector r(u,v) with respect to u and v, and dA = ||ru × rv|| dudv is the area element on the surface.

In this case, we want to evaluate the surface integral:

∫∫H 4y dA

where H is the helicoid given by the vector parametric equation:

r(u,v) = <u cos(v), u sin(v), v>, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.

The position vector r(u,v) has partial derivatives with respect to u and v given by:

ru = <cos(v), sin(v), 0>

rv = <-u sin(v), u cos(v), 1>

The area element is given by:

dA = ||ru × rv|| dudv = ||<cos(v), sin(v), u>| dudv = u dudv

Therefore, the surface integral can be written as:

\($\int\int_H 4y dA = \int_0^{9\pi} \int_0^1 4(u\sin v)u dudv$\\$= \int_0^{9\pi} \sin v \int_0^1 4u^2 du dv$\)

\($= \int_0^{9\pi} \sin v \left(\frac{4}{3}\right) dv$\\$= \left[-\frac{4}{3} \cos v\right]_0^{9\pi}$\)

= 8/3

Hence, According to the given information the value of the surface integral is 8/3.

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Answer:

m = 4

Step-by-step explanation:

We know that,

( 15 , -3 ) ⇒ ( x₁ , y₁ )

( 17 , 5 ) ⇒  ( x₂ , y₂ )

You have to use y = m x + c to find the equation of the line.

Here,

m = slope

c = y - intercept

Let find the slope now.

\(m = \frac{y_{1}-y_{2} }{x_{1}-x_{2} }\)

\(m=\frac{-3-5}{15-17}\)

\(m=\frac{-8}{-2}\)

\(m=4\)

Slope = 4

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

.022

Step-by-step explanation:

Answer on Khan

Answer:

The answer is below

Step-by-step explanation:

What is the equilibrium price and the quantity for the market whose quantity demanded and quantity supplied are given: Qd=220-5P and Qs= -20+3P?]

Solution:

The equilibrium price of a goods is the price at which the quantity of goods supplied is equal to the quantity of goods demanded. The equilibrium price can be determined by the supply and demand curve. The equilibrium price is the price at which the point of intersection of the supply and demand curve.

At equilibrium:

\(Q_s=Q_d\\\\-20+3p=220-5p\\\\220+20=3p+5p\\\\8p=240\\\\p=30\)

The equilibrium price is 30.

The equilibrium quantity = 220 - 5p = 220 - 5(30) = 70

Answer:

Roberto is correct because 15/16 x 4/5 = 3/4.

Roberto's solution to the division problem is correct, but

there are no true statements on your list of choices.

SOLUTION:

We are to find the inverse of the given function;

Answer:

4n+1

Step-by-step explanation:

Try with each expression to find the first one like. 5×1+1 is wrong because, you dont get 5 for the one, so its wrong. second one is 4×1-5 is wrong and you wont get the first answer.

the third one is the only one that actually gives the same numbers for the sequence given here.

Answer:

223

Step-by-step explanation:

328-105=223

Step-by-step explanation:

To multiply two numbers in scientific notation, you multiply their coefficients and add their exponents. Applying this rule, we get:

(4 x 10^11) (8 x 10^6) = (4 x 8) x (10^11 x 10^6) = 32 x 10^17

However, this result is not yet in scientific notation because the coefficient 32 is not between 1 and 10. To put it in scientific notation, we need to divide the coefficient by 10 and increase the exponent by 1. This gives:

32 x 10^17 = 3.2 x 10^18

Therefore, the product of (4 x 10^11) and (8 x 10^6) expressed in scientific notation is 3.2 x 10^18.

Answer:

25%were girls.

hope it helps..

Answer:

I think it's 8.5m,I wish it is correct.

Step-by-step explanation:

:)I wish it helps.

Answer:

350 m² = 70 m × breadth

Step-by-step explanation:

This will be 5m = breadth

The approach for solving for incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.

It can also be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Formula for solving incenter:

Let (x1,y1) , (x2,y2) and (x3,y3) are three points of triangle.

and a,b,c are lengths of sides.

I = ((ax1+bx2+x3 / a+b+c  ,  ay1+by2+cy3 / a+b+c))

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Step-by-step explanation:

14.99 - 11.53= 3.46+1.95 =4.41

Answer:

1 way.

Step-by-step explanation:

1) 10 Chocolate Donuts and 4 Jelly Donuts

The number of ways to select 14 donuts so that at least 5 chocolate donuts and at most 4 jelly donuts are selected are 3003.

"Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called combination. Both concepts are very important in Mathematics."

Given,

Number of varieties that are sold are 4

So the number of combinations with atleast 5 chocolate donut and most\(14C_4=\frac{14!}{4!(14-4)!} + \frac{14!}{5!(14-5)!} \\\\=1001 +2002\\\\=3003\)

Hence, the number of ways to select 14 donuts so that at least 5 Chocolate donuts and at most 4 Jelly donuts selected are 3003.

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The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

b = 4/10

Step-by-step explanation:

30/100 = 3/10 [ 0 will get cancelled]

3/10 + b = 7/10

b = 7/10 - 3/10

b = 4/10

I hope it helps u dear

Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

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Answer:

x = -2

Step-by-step explanation:

let the unknown number be x

\(9 \times x + 2 = 8 \times x \\ 9x + 2 = 8x\)

Collect like terms and simplify

\(9x - 8x = - 2 \\ x = - 2\)

The unknown number would be x = -2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have given a statement as "The sum of nine times a number, and 2, is equal to eight times the number."

Let the unknown number be x

9x + 2 = 8x

Collect like terms and simplify;

9x - 8x = -2

x = -2

Thus, the variable would be x = -2.

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Answer:

x+(x+2) = 156

Step-by-step explanation:

Let x = 1st odd integer

x+2 = next odd integer

x+(x+2) = 156

2x+2 =156

Subtract 2

2x= 154

Divide by 2

x = 77

x+2 = 79

The equation of the line is y = 2/3x + 1

The graph represents the given parameter

From the graph, we have the following points that can be used in our computation:

(x, y) = (0, 1) and (3, 3)

The equation of the line is then calculated using the following equation

y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁

Where

(x, y) = (0, 1) and (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = (3 - 1)/(3 - 0) * (x - 0) + 1

Evaluate

y = 2/3 (x - 0) + 1

So, we have

y = 2/3x + 1

Hence, the line equation is y = 2/3x + 1

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Answer:

-882y^11/x^5

Step-by-step explanation:

The exponential equation shown in the graph is the second one:

y = -3*(2)^x

We know that the graph is the graph of an exponential equation of the form:

y = a*(b)^x

Now, notice that the graph intercepts the y-axis at the value y = -3, then evaluating the equation in x = 0 we will get:

-3 = a*(b)^0

-3 = a

Then our exponential equation is of the form:

y = -3*(b)^x

There is only one with that shape, which is the second option:

y = -3*(2)^x

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°