What is 40x52 To the 7 power

Answer:

Step-by-step explanation:

If you mean √200, you cannot write it as V200.

√200 = √(10²×2) = 10√2

Answer:

B.) 2/10

Step-by-step explanation:

Step-by-step explanation:

The given equations are

x2+y3=xy9

⟹xy2y+3x=xy9

⟹3x+2y=9 ........(i) 

x4+y9=xy21

⟹xy4y+9x=xy21

⟹9x+4y=21   ........(ii)  

Now (i)×3⟶9x+6y=27   .....(iii)

Subtracting (iii) from (ii),

−2y=−6⇒y=3.

Putting y=3 in (i),

3x+2×3=9⟹x=1.∴(x,y)=(1,3)

Answer:

i

Step-by-step explanation:

The mass of the tow chain will be equal to 12.96 kg.

The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.

Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.

The mass of 1 m chain = 2.16 kg

Mass of 6-meter chain = 2.16 x 6

Mass of 6-meter chain = 12.96 kg

Therefore, the mass of the tow chain will be equal to 12.96 kg.

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Answer:

The slope is m=2.145.

The y-intercept is b=-1.33.

Step-by-step explanation:

We have this data:

- The mean and standard deviation for x are 5.43 and 1.12, respectively.

- The mean and standard deviation for y are 10.32 and 2.69, respectively.

- The correlation is 0.893.

We have to calculate the slope and the y-intercept of the least-squares line.

With the given data, we can calculate the slope m as:

\(m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145\)

Then, the y-intercept is calculated as:

\(b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33\)

Answer:

ya-yb=yc+ca

Step-by-step explanation:

Distribute y and c to the values inside the parenthesis.

ya-yb=yc+ca

Answer:

Jenna got a better score

Step-by-step explanation:

She got a better score because Marcus missed 2 but Jenna only missed one.

Answer:

Area = ab sinx

Area = (8)(18) sin32

Area  = 144 sin32

Area = 79.41

Answer:

x is 54˚

Step-by-step explanation:

Answer:

x = 54°

Step-by-step explanation:

Forming the equation,

→ (2x + 2)° = (3x - 52)°

Now the value of x will be,

→ (2x + 2)° = (3x - 52)°

→ 2x - 3x = -52° - 2°

→ -x = -54°

→ [ x = 54° ]

Hence, the value of x is 54°.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

Answer:

How many general admission tickets were​ purchased? __136__

How many upper reserved tickets we purchased? _300_

Step-by-step explanation:

Let the number of general tickets = g.

Let the number of reserved tickets = r.

6.5g + 8r = 3284

g + r = 436

     6.5g + 8r = 3284

(+)   -8g + -8r = -3488

--------------------------------

     -1.5g         = -204

g = 136

g + r = 436

136 + r = 436

r = 300

Answer:

How many general admission tickets were​ purchased? __136__

How many upper reserved tickets we purchased? _300_

Answer:

136 general admission tickets were purchased

300 upper reserved tickets were purchased

Step-by-step explanation:

This is a classic system of equations problem. Let the number of general admission tickets sold be \(g\) and the number of reserved tickets sold be \(r\). We can write the following system of equations:

\(\begin{cases}6.50g+8.00r=3284,\\g+r=436\end{cases}\)

Multiply the second equation by -8 and add both equations to isolate \(g\):

\(-8(g+r)=-8(436),\\-8g-8r=-3488,\\\begin{cases}6.50g+8.00r=3284,\\-8g-8r=-3488\end{cases},\\-1.5g=-204,\\g=\frac{-204}{-1.5}=\boxed{136}\)

Now substitute \(g=136\) into \(g+r=436\) to find the number of reserved tickets sold:

\(g+r=436,\\136+r=436,\\r=436-136=\boxed{300}\)

The circles that have their centers on the x-axis are A and C.

To determine which of the given circles have their centers on the x-axis, we need to examine the equation of the circle in each case and determine whether the y-coordinate of the center is equal to zero.

A. (x-0)² + (y-0)² = 25:

The center of the circle is at the point (0,0), which lies on the origin, which is the point where the x and y axes meet. Therefore, this circle has its center on the x-axis.

B. (x-0)² + (y-5)² = 49:

The center of the circle is at the point (0,5), so the y-coordinate of the center is 5 which is not equal to zero. Therefore, this circle does not have its center on the x-axis.

C. (x-4)² + (v-0)² = 22:

The center of the circle is at the point (4,0), so the y-coordinate of the center is 0. Therefore, this circle has its center on the x-axis.

D. (x + 1)² + (y-7)² = 16:

The center of the circle is at the point (-1,7), so the y-coordinate of the center is 7 which is not equal to zero. Therefore, this circle does not have its center on the x-axis.(option-a,c)

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The number of text messages sent by Megan in the month of August are 820.

Given that :-

Money owed by Megan = $26

She can send first 650 messages for $9

For 10 additional text messages, $1 is spent.

We have to find the number of text messages sent by her in the month of august.

We know that,

Money left after sending 650 messages  = $26 - $9 = $17

Hence, by simple multiplication, we can say that,

Number of text messages sent after sending 650 messages = 17*10 = 170

Total number of text messages sent by Megan = 650 + 170 = 820.

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Count the multiples of 12:

⌊1000/12⌋ = 83

(where ⌊x⌋ denotes the "floor" of x, or the largest integer that is less than or equal to x)

These are the integers

{12, 24, 36, 48, …, 996}

Count the multiples of 15:

⌊1000/15⌋ = 66

These are

{15, 30, 45, 60, …, 990}

Count the multiples of both 12 and 15; these are multiples of LCM(12, 15) = 60:

⌊1000/60⌋ = 16

These are

{60, 120, 180, 240, …, 960}

Now use the inclusion/exclusion principle to count the multiples of either 12 or 15, but not both:

83 + 66 - 2•16 = 117

Among the multiples of 12 and the multiples of 15, we count the numbers that are multiples of both 12 and 15. By subtracting the number of multiples of both (16), we get the count of integers that are either divisible by 12 or 15. We subract 16 again to remove those that are divisible by both 12 and 15.

Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.

Total interest is determined by the addition of all the interest payments.

United bank offers mortgage at an APR of 4.2%

APR means annual percentage rate.

mortgage is offered for the period of 15 years.

initial principal amount of Marcy = $120000

we need to determine the monthly payment from United bank.

at first, we will determine the rate of interest per month.

monthly interest rate = (4.2) / (100 × 12) = 0.0035

1 year = 12 months

15 years = 15×12 = 180 months

monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal

monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000

                          = $1207.70

from united bank monthly payment = $1207.70

Now we calculate the monthly payment from Capitol bank.

APR for capitol bank = 4.5%

number of years for which mortgage is issued = 25 years

number of months = 12×25 = 300.

monthly interest rate = (4.5) / (100×12) = 0.00375

monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000

                 = 1834.62

monthly payment from Capitol bank = $1834.62

total interest from Capitol bank = principal money × yearly interest rate × time period.

Total interest = 120000 × 4.5/100× 25

                        = $135000 for the Capitol bank

Total interest from United bank = principal amount × yearly interest × time period

            = 120000× 4.2/100 × 15

total interest from united bank   = $75600

United bank has lower total interest.

difference in monthly payment = 1834.62 - 1207.70

                                                   = 626.92 dollars

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Answer:

30.

Step-by-step explanation:

The sides of each square  = √25 = 5.

Therefore the longest side of the rectangle is 2*5 = 10 and the shortest = 5.

Perimeter = 2*10 + 2*5 = 30.

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

9514 1404 393

Answer:

  3.6481 years

Step-by-step explanation:

The doubling time is not a function of the amount invested. It can be found by considering the account balance multiplier:

  2 = e^(rt) = e^(0.19t)

Taking logs, we can solve for t:

  ln(2) = 0.19t

  t = ln(2)/0.19 ≈ 3.6481431

Rounded to 4 decimal places, the doubling time is 3.6481 years, for either balance.

The value of GH is 93.

Given,

Point G is the midpoint of segment FH.

GH= 16x-19 and FG=12x+9.

We need to find GH.

If there is a midpoint between two points the midpoint divided the line between two points into two equal lengths.

Example:

A ________B__________C

AB = BC

We have,

F_______G_______H

G is the midpoint.

GH= 16x-19

FG=12x+9.

FG = GH

16x-19 = 12x+9

16x - 12x = 9 + 19

4x = 28

x = 7

Now,

GH = 16x - 19

      = 16 x 7 - 19

      = 112 - 19

     = 93

Thus the value of GH is 93.

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Answer:

  1/14

Step-by-step explanation:

In the given geometry, we have similar triangles:

  ΔCEF ~ ΔBEA ~ ΔDAF

This lets us write the relations for corresponding sides ...

  CF/CE = DF/DA

where DF = CF -CD

We can rearrange this relation to give the value we're looking for as follows.

__

Making the substutition for DF, and multiplying by CE, we have ...

  CF = CE(CF -CD)/DA

Both DA and CD are sides of the rhombus, so are both 14 cm in length. Multiplying by DA and making the number substitution, we have ...

  DA·CF = CE·CF -CE·CD

  14·CF = CE·CF -14·CE . . . . substitute 14 for DA and CD

  14(CF +CE) = CE·CF . . . . . add 14·CE

  (CF +CE)/(CE·CF) = 1/14 . . . . divide by 14·CE·CF

  1/CE +1/CF = 1/14 . . . . . . . . . simplify

is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

Answer:

24

Step-by-step explanation:

96/8 + {2(5-7) exponent 2 + 4}

= 96/8 + {2(-2) exponent 2 + 4}

= 96/8 + {2(4) + 4}

= 12 + {8 + 4}

= 12 + 12

=24

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

-9

Step-by-step explanation:

The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the points through which the line passes: (-3,-7) and (-3,10).

The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3

Hence, the two lines  lie on a vertical line.

since the slope of the vertical line is undefined.

The equation of the line passing through these two points is simply the equation of the vertical line:

x = -3

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Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

An expression that is equivalent to –5(x–8)+32 is -5x + 72.

What is an expression ?

To generate an equivalent expression for –5(x–8)+32, we can simplify the expression using the distributive property of multiplication over addition/subtraction.

Starting with -5(x-8), we can distribute the -5 across the parentheses by multiplying it by each term inside the parentheses. This gives us:

-5(x-8) = -5x + (-5)(-8)

Simplifying further, we get:

-5(x-8) = -5x + 40

Now we can substitute this expression back into the original equation:

-5(x-8) + 32 = (-5x + 40) + 32

Simplifying further, we get:

-5(x-8) + 32 = -5x + 72

Therefore, an expression that is equivalent to –5(x–8)+32 is -5x + 72.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are grouped together to represent a mathematical relationship or operation. An expression can contain one or more terms, which are separated by mathematical operators such as addition, subtraction, multiplication, division, and exponentiation.

Expressions can be used to represent a wide variety of mathematical concepts, such as equations, inequalities, functions, and formulas. They can be evaluated or simplified to obtain a numerical or algebraic result, or they can be manipulated and transformed using mathematical rules and properties.

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