On a map where each unit represents 100 miles, two airports are located at P(1,17) and Q(12,10). What is the distance, to the nearest whole mile, between the two airports? A. 1,800 miles B. 1,304 miles C. 1,122 miles D. 900 miles

The value of x if the volume and 6 by the area of one face are equal is 6

The side length of the cube is given as

Side length = x

From the question, we have the statement to be

The volume of the cube and 6 times the area of one of its faces have the same value.

The volume of a cube with side length x is

V = x³

The surface area multiplied by 6 is

A = 6x²

When both have the same values, we have

x³ = 6x²

Divide both sides by x²

x = 6

Hence, the value of x is 6

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Answer:

the factors are:  1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 643, 660, 1286, 1929, 2572, 3215, 3858, 6430, 7073, 7716, 9645, 12860, 14146, 19290, 21219, 28292, 35365, 38580, 42438, 70730, 84876, 106095, 141460, 212190, 424380.

Step-by-step explanation:

\(\huge \bf༆ Answer ༄\)

For the given triangles to be congruent by SSS criterion, the sides HJ and LN should be equal ~

therefore correct choice is ~ C

\( \large \boxed{ \sf \: HJ \cong LN}\)

The additional information needed to prove that both triangles are congruent by the SSS Congruence Theorem would be: C. HJ ≅ LN

Recall:

Thus, in the two triangles given, the two triangles has:

Therefore, an additional information needed to prove that both triangles are congruent by the SSS Congruence Theorem would be: C. HJ ≅ LN

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Answer:

L.H.S = R. H.S

Step-by-step explanation:

Hope, you see the image .

Note; Way to solve question may vary according to your grade

This process is for grade 9 and above

For lower level you can express all tri.. ratios in p , b & h and prove it

Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Answer:

(a) \(4\frac{1}{5}\)

(b)  \(7\frac{7}{24}\)

Step-by-step explanation:

One way of operating with mixed numbers is to first convert them into improper fractions, and operate with them following the simple rules of fraction multiplication, and at the end convert the answer into mixed number.

(a) For this operation let's first convert \(5\,\frac{2}{5}\) into an improper fraction:

\(5\frac{2}{5} =5+\frac{2}{5} =\frac{25}{5} +\frac{2}{5} =\frac{27}{5}\)

Now perform the requested operation:

\(\frac{7}{9} \,*\,\frac{27}{5} =\frac{189}{45} =\frac{21}{5} =4\frac{1}{5}\)

(b) Start by converting both mixed numbers into improper fractions and then operate as indicated:

\(1\frac{3}{4} =\frac{4+3}{4} =\frac{7}{4} \\4\frac{1}{6} =\frac{24+1}{6} =\frac{25}{6}\)

\(\frac{7}{4} *\frac{25}{6} =\frac{175}{24} =7\frac{7}{24}\)

By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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Step-by-step explanation:

ur awnser is b!

The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Answer: x=2.

Step-by-step explanation:

\(\displaystyle \\25^{x-1}=5^{2x-1}-100\\\\(5^2)^{x-1}=\frac{5^{2x}}{5} -100\\\\5^{2*(x-1)}=\frac{5^{2x}}{5} -100\\\\5^{2x-2}=\frac{5^{2x}}{5}-100\\\\\frac{5^{2x}}{5^2} =\frac{5^{2x}}{5} -100\\\\\frac{5^{2x}}{25} =\frac{5^{2x}}{5} -100\ |*25\\\\5^{2x}=5*5^{2x}-2500\\\\5^{2x}+2500=5*5^{2x}-2500+2500\\\\5^{2x}+2500=5*5^{2x}\\\\5^{2x}+2500-5^{2x}=5*5^{2x}-5^{2x}\\\\2500=4*5^{2x}\ |:4\\\\625=5^{2x}\\\\5^4=5^{2x}\ \ \ \ \ \ \Rightarrow\\\\4=2x\ |:2\\\\2=x\\\\Hence\ \ x=2.\)

Answer:

$6.3

Step-by-step explanation:

Original price = $18

Percentage Discount = 65%

Discount = 18*65% = 18*0.65 = $11.7

Sale Price = Original price - Discount

= $18 - $11.7

= $6.3

Answer:

81.5

Step-by-step explanation:

<G and <H are congruent

<F and <I are congruent

so the last two angles in both triangles must also be congruent

this means that <K and <J are congruent

so we can create this equation: <K = <J

substitute the angles with what we know: 4\(y^{2}\) = 6\(y^{2}\) - 40

add 40 to both sides and subtract 4\(y^{2}\) from both sides: 40 = 2\(y^{2}\)

you get: 20 = \(y^{2}\)

root square on both sides: \(\sqrt{20}\) = \(\sqrt{y^{2} }\)

you get: y ≈ 4.5

substitute this into one of the equations for a missing variable:

6\(y^{2}\) -----> 6 (4.5 x 4.5) - 40

6 ( 20.25) - 40

121.5 - 40

81.5

Answer:

3.23/5=.646

.646*7=4.522

rounded is $4.52

Step-by-step explanation:

Answer:

Total amount pay for new apartment = $4,740.75

Step-by-step explanation:

Find:

Total amount pay for new apartment

Computation:

Particular                                       Amount

Monthly rent of apartment           $1,650

Add:

Application fee [1,650 x 1.5%]      $24.75

Credit application fee                   $30

Security rent                                  $1,650

Broker's fee [1,650 x 12 x 7%]      $1,386

Total                                               $4,740.75

Total amount pay for new apartment = $4,740.75

Answer:

45 students

Step-by-step explanation:

40+40=80   40/2=20   80+20=100

18+18=36      18/2=9       36+9=45

horrible explaining but hope it helps :)

Answer:

45

Step-by-step explanation:

18 ÷ 45 = 0.4 = 40%

Answer:

b can I have

Step-by-step explanation:

Answer:

time = 70 minutes

Answer:

x-4y=8

Step-by-step explanation:

x-4y=8

-4y=-x+8

y =-x/4 + 2

Step-by-step explanation:

the cost of 1 kg mangoes = 147/ 5

= Rs. 29.40

mark me as brainliest

Answer:

cost of 1 kg mango = rupees 29.4

Step-by-step explanation:

cost of 5 kg mangoes =rupees 147

cost of 1 kg mango =?

Now, lets find cost of 1 kg mangoes

CP od 1 kg mangoes = cost of 5 kg mangoes/5 kg

=rupees 147/5

=rupees 29.4

Answer:

Bank A will exchange it

Step-by-step example

Answer:

Step-by-step explanation:

First we need the length of the hypotenuse.

20^2 + 21^2 = c^2

400 + 441 = c^2

841 = c^2

29 = c

If you are using angle B as your theta (angle from which the relations are formed:

a) sin = O/H = 20/29

b) cos = A/H = 21/29

c) tan = O/A = 20/21

Answer:

The company will need 3,360 inches of wax

Step-by-step explanation:

To find how much wax you need per one candle you would do 6in.X4in. which gives you 24in. of wax. Then to find the amount of was for 140 candles you would do 140X24in. to get 3,360 inches of wax.

We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix

Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.

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Answer:

x=7

Step-by-step explanation:

Step #1- Set the two lines equal to each other

10+12=x+15

Step #2- Solve for the line you have all values for

10+12=22

Step#3- Plug 22 back into the equation where the two lines are set equal to each other

22=x+15

Step #4- Solve for X algebraically

22=x+15

22-15=x

7=x

Answer:

B

Step-by-step explanation:

3 x 10 ^17

Which is B

edit: So when doing scientific notation, you just divide the important first number of 9.3 or whatever by 3.1 like normal.

Then, when doing exponents, heres a rule of thumb.

When adding exponents, the base must be the same.

9.3 ^ 100  +  9.3 ^ 3  =  9.3 ^103

9.3 ^ 29 + 4.4 ^ 54 = cannot be solved

When subtracting exponents, the same rule applies as adding, the bases must be the same, otherwise, you just subtract or add like normal.

When dividing exponents, you just subtract exponents. The bases must be the same though of course.

3 ^ 30

----------

3 ^ 20

====  3 ^ 10

When multiplying exponents, you add exponents like normal. Bases are the same ect.

4 ^ 49    x    4 ^ 2   =   4 ^ 51

When doing scientific notation, the same rule applies.

The 10 is the base, so in your case, you divide the 9.3 and 3.1 like normal to get 3.

The exponent by the 10 is subtracted to get 17 since 34 - 17 = 17.

Option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.

We are given that:

Jeffrey has 8 worms

The 4 worms in it has the length of 3 inches.

The expression would become:

Length = 4 × 3

Also, we are given that the rest 4 worms are of equal length.

Let that equal length be x

The expression becomes:

Length = 4 × x = 4 x

Also, we are given that the total length of the worms = 32 inches.

The equation becomes:

32 = 3 × 4 + 4 × x

4 ( x + 3 ) = 32

Therefore, option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.

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The probability for the particle to exist between x=0 and x=L/3, when the quantum number n=3, is 1/9.

In quantum mechanics, a particle in a one-dimensional box of length L can only occupy certain discrete energy levels determined by the quantum number n. The energy levels are given by the equation En = (\(n^2\) * \(h^2\))/(8m\(L^2\)), where h is Planck's constant and m is the mass of the particle.

Given that the quantum number n = 3, we can determine the energy associated with this level as E3 = (\(3^2\) * \(h^2\))/(8m\(L^2\)).

The probability of finding the particle between x=0 and x=L/3 corresponds to the portion of the total probability density function (PDF) within that range. The PDF for a particle in a box is given by P(x) = |ψ\((x)|^2\), where ψ(x) is the wave function.

For the ground state (n = 1), the wave function is a sin(xπ/L) and the corresponding PDF is proportional to \(sin^2\)(xπ/L). For n = 3, the wave function becomes sin(3xπ/L), and the corresponding PDF is proportional to\(sin^2\)(3xπ/L).

To find the probability, we integrate the PDF from x=0 to x=L/3, which is equivalent to calculating the area under the PDF curve within that range. In this case, the integral is ∫[0 to L/3] \(sin^2\)(3xπ/L) dx.

Evaluating this integral gives us a result of 1/9, indicating that there is a 1/9 probability of finding the particle between x=0 and x=L/3 when the quantum number n=3.

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