This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?

Answer: \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Step-by-step explanation:

The given expression: \(\sqrt{\dfrac{16n}{m^3}}\)

'

since \(16=4^2\)

\(m^3=m^{2+1}= m^2\times m\)   [\(a^{n+m}=a^n\times a^m\)]

Now, the given expression becomes,

\(\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}\)

Since there is root in denominator , so we need to rationalize

\(\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}\)

Hence, the correct option is \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Answer:

3x + 5.

Step-by-step explanation:

factor out 1/6 (1/2 • 1/3)

distribute the 3 from the paranthesis

1/6 (3(8x + 4) + 2(9-3x))

1/6(24x + 12 + 2(9-3x))

distribute 2 through parentheses

1/6(24x+12+18-6x)

collect like terms:

1/6(18x + 12 + 18) > 1/6(18x +30)

factor out 6

1/6 • 6(3x+5)

reduce with GCF (6)

3x + 5

Answer:  The simplified expression is:  " \(3x + 5\) " .

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Step-by-step explanation:

______________________________

Given the expression:

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" One-half (8 x + 4) + one-third (9 minus 3x) "  ;

We can rewrite that as:

\(\frac{1}{2}\) \((8x+4) + \frac{1}{3}(9-3x)\)

Now, let us simplify the expression:

Start with:

\(\frac{1}{2}(8x+4)\) ;

Note the "distributive property" of multiplication:

  a(b + c)  = ab + ac ;

Likewise:

\(\frac{1}{2}{(8x +4) = (\frac{1}{2})8x + (\frac{1}{2})4=\frac{8}{2}x +\frac{4}{2} =4x +2\) ;  '

Now continue with the remaining part of the expression:

\(+\frac{1}{3}(9-3x)\) ;

Again, use the "distributive property" of multiplication:

     a(b + c)  = ab + ac ;

\(+\frac{1}{3}(9-3x)= (\frac{1}{3})9+(\frac{1}{3})(-3x)=\frac{9}{3}+(-\frac{3}{3}x)=3+(-1x);\)

                                                                          =  3 − 1x ;

                                                                          =  3 − x  ;

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Now, combine both terms within the expression; to simplify the expression:  

   \((4x + 2) + (3 -x)\) ;

Rewrite as:

   \(4x + 2 + 3 - x\) ;

Now, combine the "like terms":

  \(^+4x -x = 4x -1x = 3x\) ;

  \(^+2 +3 = 5\)  ;

The simplified expression is:  " \(3x + 5\) " .

________________________________________

Hope this is helpful to you!  Best wishes!

_________________________________________

Answer:

95$

Step-by-step explanation:

Since there are 5 premium channels, we multiply the rate of charges by the number of premium channels to get the extra payment.

5 channels x 12$ per channel = 50$  

Now we add this to 35 since C= 35 + 12 or 35 plus the premium channel costs

35$ + 50 = 95$

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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Answer: 6

Step-by-step explanation: since this is a right triangle, you can use pythagorean theorem to solve this. which is a^2 + b^2 = c^2

lets say a=5 and b=root11

you would plug this into the equation -> (5)^2 + (root11)^2 = 25 + 11 which is 36 which is c^2. to get c from c^2, you'd take the square root of c^2 (which in this case is 36) to give you 6.

6 is the length of the third side

Answer:

See below.

Step-by-step explanation:

6.)

y - 2 = 3(x - 6)

y - 2 = 3x - 18

y = 3x - 16

4.)

y - (-2) = 3(x - 5)

y + 2 = 3x - 15

y = 3x - 17

3.)

y - 7 = 2(x - 4)

y - 7 = 2x - 8

y = 2x - 1

Answer:

-8

Step-by-step explanation:

midpoint = (W + X)/2

midpoint = [-11 + (-5)]/2

midpoint = -16/2

hence midpoint = -8

Answer:

Area of the square base = 100cm²

Surface area of square pyramid= 380cm²

Step-by-step explanation:

Area of the square base= L × L

= 10cm × 10cm

= 100cm²

The surface area of square pyramid= Area of the base + Area of the triangles forming the pyramid.

= 100cm² + 280cm²

If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10

According to the rule of triangle the sum of first angle and second angle should be greater than the third angle.

first angle+ second angle > third angle

Here

22-13 = 9

so to became a triangle the minimum value of the third side will be 10(9+1).

Therefore, If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10

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The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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Answer:9x1016

Step-by-step explanation:

when adding or subtracting in standard form (aka scientific notation), the powers of 10 need to be the same. If they are just add the numbers and keep the same power of 10

#2xx10^(16)+7xx10^(16)

= ( 2 + 7 ) × 10 16

9 × 10 16

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115

According to the statement

we have to find that the what percent of the population has an iq over 115.

And from given information,

the mean iq score is 100 and the standard deviation is 15.

And

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

And by use of this formula, we find the percentage of the population has an iq over 115.

Then the result will comes as 100%.

hence, 100%-Norm.Dist(value,mean,sd,true)

So, The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115.

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The calculated equation of the line L is y = -4x  + 5

Given that

We have the partition to be

m : n = 2 : 3

The coordinate is then calculated as

M = 1/(m + n) * (mx₂ + nx, my₂ + ny₁)

So, we have

M = 1/5 * (2 * 11 + 3 * -9, 2 * 12 + 3 * 7)

Evaluate

M = (-1, 9)

The slope of line PQ is

Slope = (12 - 7)/(11 + 9)

So, we have

Slope = 1/4

The slopes of perpendicular lines are opposite reciprocals

So, the slope of L is

m = -4

The equation of line L is then calculated s

y - 9 = -4(x + 1)

So, we have

y = -4(x + 1) + 9

Evaluate

y = -4x  + 5

Hence, the equation of line L is y = -4x  + 5

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Answer:

x = 43

Step-by-step explanation:

3x + 7 = 136

3x = 129

x = 43

The city of Newport, Rhode Island as the location for the sailboat race. Newport is an ideal choice for several reasons. Firstly, Newport has a rich sailing heritage and is renowned for hosting prestigious sailing events, including the world-famous America's Cup.

Secondly, Newport offers exceptional sailing conditions. It is situated on the picturesque coast of New England, providing a stunning backdrop for the race. The area benefits from consistent winds and challenging tidal currents, making it an exciting and competitive racecourse. Sailors from around the world are drawn to Newport for its unique sailing experience.

Moreover, Newport offers excellent infrastructure and facilities for sailboat racing. The city has a well-established marina with ample berthing space and modern amenities. It also boasts a vibrant waterfront community, with a range of hotels, restaurants, and shops that cater to sailors and race enthusiasts. The presence of these amenities ensures a comfortable and enjoyable experience for participants and spectators alike.

Overall, selecting Newport as the race location not only aligns with the city's sailing legacy but also guarantees a challenging and captivating race for all involved. Its favorable sailing conditions and well-developed infrastructure make it an ideal choice to showcase my skills and compete against top sailors in a highly competitive environment.

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Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

The perimeter of the updated blueprint would be = 62units.

The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.

To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;

= 10+4+2+4+2+4+10+2+2+8+2+2

= 62 units.

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Answer:

2

Step-by-step explanation:

add

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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The result of Multiplying 138.2 km by 3.5 km is 483.7 km².

To perform the indicated calculation, we need to multiply 138.2 km by 3.5 km.138.2 km x 3.5 km = 483.7 km²

The result of multiplying 138.2 km by 3.5 km is 483.7 km².

When dealing with significant figures, we should consider the least precise measurement involved in the calculation, which in this case is 3.5 km (with two significant figures). Therefore, we should round the answer to the same number of significant figures, resulting in 480 km².

So, rounding according to the rules for significant figures, the result of the calculation 138.2 km x 3.5 km is approximately 480 km².

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:  9 - 6n6n - 9(6 + n) - 99 - (6 + n)

Answer:

400

Step-by-step explanation:

403.1 rounded is 400

In a heap, the height is defined as the number of edges on the longest path from the root to a leaf node. The height of a heap with n elements is at most log₂(n+1).

To find the minimum and maximum numbers of elements in a heap of height h, we can use the formula:

The minimum number of elements in a heap of height h is 2^h (a complete binary tree of height h with the minimum number of nodes).

The maximum number of elements in a heap of height h is 2^(h+1) - 1 (a complete binary tree of height h with the maximum number of nodes).

Therefore, the minimum and maximum numbers of elements in a heap of height h are:

Minimum: 2^h

Maximum: 2^(h+1) - 1

Note that not all values of h are valid heap heights. A heap must be a complete binary tree, so its height can only take on values that satisfy the formula: \(h < = log₂(n+1),\)where n is the number of elements in the heap.

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The real values of theta for which (4+3i)/(1-2i) is purely real are given by theta = n*pi, where n is an integer.

To find the real values of theta for which the complex number (4+3i)/(1-2i) is purely real, we need to eliminate the imaginary part of the expression by multiplying the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of 1-2i is 1+2i, so we can write:

(4+3i)/(1-2i) * (1+2i)/(1+2i)

Simplifying this expression, we get:

(4+3i)(1+2i)/(1+4)

(4+3i)(1+2i)/5

Expanding the numerator of this expression using FOIL, we get:

(4*1)+(4*2i)+(3i*1)+(3i*2i) / 5

(4+8i+3i-6)/(5)

(-2+11i)/5

For this expression to be purely real, we need the imaginary part of (-2+11i)/5 to be equal to zero.

Setting the imaginary part to zero, we get:

11/5 * sin(theta) = 0

Solving for theta, we get:

sin(theta) = 0

This occurs when theta is an integer multiple of pi, or in other words:

theta = n*pi, where n is an integer.

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Answer:

3+4

Step-by-step explanation:

cuz they are separated by a plus sign

Answer

he diameter of the circle is 22 units.

x² + y² - 16x + 12y = 21    

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Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)