Solve the literal equation for x.
y=5x-rx-5

Answer:

8.9 cm

Step-by-step explanation:

We have
\(\overline {UV} = 16.8 cm\\\\\overline {WV} = 7.9 cm\\\\ Since all lines are scalars, \overline{WV} = \overline{VW}\\\textrm{We see that \overline{UW} + \overline{WV} = \overline{UV}\\\\\overline {UW} \\ = \overline {UV} - \overline {WV} = 16.9 - 7.9 = 8.9 cm}\)

\( \frac{7}{9} \times (8 \frac{3}{7} + 5 \frac{11}{14}) = \\ \)

\( \frac{7}{9} \times (8 \frac{6}{14} + 5 \frac{11}{14} ) = \\ \)

\( \frac{7}{9} \times (13 \frac{6 + 11}{14}) = \\ \)

\( \frac{7}{9} \times (13 \frac{17}{14}) = \\ \)

\( \frac{7}{9} \times (14 \frac{3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{14 \times 3 + 3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{42 + 3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{45}{14}) = \frac{7 \times 45}{9 \times 14} = \frac{5}{2} \\ \)

_________________________________

And we're done.

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Answer:

\(\displaystyle \frac{199}{18}\)

Step-by-step explanation:

Fraction Operations

Before attempting to operate with the given fractions, we need to express all of them in the form a/b, because the last 2 fractions are in mixed form.

\(\displaystyle 8\frac{3}{7}=8+\frac{3}{7}=\frac{8*7+3}{7}=\frac{59}{7}\)

\(\displaystyle 5\frac{11}{14}=5+\frac{11}{14}=\frac{5*14+11}{14}=\frac{81}{14}\)

Now for the sum of the last two fractions:

\(\displaystyle \frac{59}{7}+\frac{81}{14}\)

Make both denominators equal by multiplying by 2 both parts of the first fraction:

\(\displaystyle \frac{59}{7}+\frac{81}{14}=\frac{118}{14}+\frac{81}{14}\)

\(\displaystyle =\frac{118+81}{14}=\frac{199}{14}\)

Now multiply by 7/9:

\(\displaystyle \frac{199}{14}*\frac{7}{9}=\frac{199}{18}\)

There are 161 feet are in 53 yards, 2 feet.

Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.

As we know that;

1 yard = 3 feet

53 yards = 3 ×53 feet

53 yards = 159 feet

53 yards, 2 feet = 159 feet + 2 feet

53 yards, 2 feet = 161 feet

Hence, there are 161 feet in 53 yards, 2 feet.

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Answer:

Slope = -1

Step-by-step explanation:

There is ways a 1 in front of an x if there is no other number

The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units

From the graph, the vertices of the land are

A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)

Calculate the distance between adjacent vertices

So, we have

AB = √[(0 - 25)² + (20 - 19)²] = 25.02

BC = √[(20 - 25)² + (2 - 19)²] = 17.72

DC = √[(20 - 5)² + (2 - 0)²] = 15.13

AD = √[(0 - 5)² + (20 - 0)²] = 20.62

The perimeter of the plot land is

P = 25.02 + 17.72 + 15.13 + 20.62

P = 78.49 units

This is calculated as

Area = Plot land - Building - Parking lot

Using the vertices, we have

Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]

This gives

Area = 295 -  45 - 40

So, we have

Area = 210

Hence, the area is 210 square units

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The interval containing the middle-most76% of sample means  \(102.836 < \mathrm{x} < 137.164\).

As per the data given in the above question,

A distribution of values is normal with a mean of \(\mu=120\).

A standard deviation of \(\sigma=21\).

Drawing samples of size n=13.

The middle-most76% of sample means.

Find the interval containing the middle-most76% of sample means?

\(\mathrm{P}(-\mathrm{z} < \mathrm{x} < \mathrm{z})=0.76\\\mathrm{P}(\mathrm{x} < \mathrm{z})-\mathrm{P}(\mathrm{x} < -\mathrm{z})=0.76\\\)

Further

\(\mathrm{P}(\mathrm{x} < -\mathrm{z})=\mathrm{P}(\mathrm{x} > \mathrm{z})\)

\(\mathrm{P}(\mathrm{X} < \mathrm{Z})-\mathrm{P}(\mathrm{X} > \mathrm{Z})=0.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})-1+\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.46\\2 \mathrm{P}(\mathrm{X} < \mathrm{Z})=1.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.88\)

\(= NORMSINV (0.73)\\\mathrm{Z}=0.613\)

\(& \mathrm{X}=\mathrm{z} \sigma+\mu \\& \mathrm{X}=0.613 \times 28+120 \\& \mathrm{X}=137.164-\mathrm{x} & =\mu-\mathrm{z} \sigma \\-\mathrm{x} & =120-0.613 \times 28 \\-\mathrm{x} & =102.836\)

Now the interval sample is as follow,

\(102.836 < \mathrm{x} < 137.164\)

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is the sum of the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied.

The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is calculated by summing the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied. Momentum is a vector quantity which is equal to the product of the mass and velocity of an object. In this case, the t-shirt has a mass of 4 kg and a velocity of 4 m/s. The force of 15 N applied to the t-shirt for 3 seconds causes the t-shirt to accelerate, increasing its velocity from 4 m/s to 8 m/s. This increase in velocity results in an increase in the momentum of the t-shirt from 2 kg⋅m/s to 17.5 kg⋅m/s. Thus, by calculating the change in momentum due to the applied force, we can determine the final momentum of the t-shirt.

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The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Here,

An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.

The distance between two complex numbers a + bi and c + di can be found using the formula:

√((c - a)² + (d - b)²)

So, the distance between 3-2i and 6-i is:

√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10

And the distance between 3-2i and c is:

√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)

Since these distances must be equal, we have:

√((c - 3)² + (c + 2)²) = √10

Squaring both sides:

(c - 3)² + (c + 2)² = 10

Expanding both sides:

c² - 6c + 9 + c² + 4c + 4 = 10

Combining like terms:

2c² + 10c + 5 = 10

Subtracting 10 from both sides:

2c² + 10c - 5 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

c = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 10, and c = -5. Plugging these values into the formula:

c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2

c = (-10 ± √(100 + 40)) / 4

c = (-10 ± √(140)) / 4

c = (-10 ± 10√2) / 4

So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.

The product of these two solutions is:

c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)

= (100 - 100√2 + 100) / 16

= (200 - 100√2) / 16

(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

74 and 76

Step-by-step explanation:

I'm pretty sure

Answer:

8 and 9

Step-by-step explanation:

8 x 8 = 64

9 x 9 = 81

75 is the number between 64 and 81

Answer:

1035.75

Step-by-step explanation:

Answer:

your answer is 168 adult tickets

Step-by-step explanation:

Just got 100 on edge

Answer:

C

Step-by-step explanation:

It is the graph of f(x) translated 3 units down. Think about in numerical terms,

if      y = 5     y-1  = 5- 1 = 4, so that's what is happening with all numbers on the y axis. You have y = f(x) and you do y-3 = f(x)-3, so, all "y" points are translated 3 units down

The number of months to reach 51 can be illustrated as 3060 - 100x = 51.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.

The farmer planted 3,060 tomato plants in his garden.

Let's assume there's a decrease of 100 monthly.

The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c

This will be:

3060 - 100x = 51.

This illustrates the equation for the number of months.

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A fair coin has 2 sides.

Flipping three fair coins means a total of 2^3 = 8 outcomes.

We are interested in getting two tails and a head which can happen in 3 ways.

{HTT, THT, TTH}

Odds in favor means favorable outcomes : unfavorable outcomes

Odds against means unfavorable outcomes : favorable outcomes

For the given case, we have

Favorable outcomes = 3

Unfavorable outcomes = 8 - 3 = 5

The odds against of getting two tails and a head are 5:3

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

-6y + 6 = -2(3y - 3)

Step-by-step explanation:

-6y + 6 = -2(3y - 3)

-6y + 6 = -6y + 6

Therefore, the equation has infinitely many solutions.

Answer:

.

Step-by-step explanation:

.

Answer:

-15.874507866387544

Step-by-step explanation:

I used a calculator to find the square root of 252 then I just added a negative sing in front of it.

Answer:

Multiplication

I hope this helps!

Answer:

First - y=-2x+3

Second - y=-7+3

Step-by-step explanation:

Answer:

Y= -2 x + 3

Y= 3 x + -7

Step-by-step explanation:

Answer: The correct answer is C

x-1/8y^2=0

Step-by-step explanation: i took the test and got it right

Answer:

20) 8 years

21) Tori could paint the room alone for 3 hours, Sydney could paint the room alone for 5 hours.

Step-by-step explanation:

A = P ( 1 + r/n ) ^ nt.

8000 = 5000 ( 1 + 6%/4) ^ 4t

8000 = 5000 ( 1 + 0.06/4) ^4t

8000 = 5000 ( 1 + 0.015 ) ^ 4t

8000 = 5000 ( 1.015 ) ^ 4t

8000 / 5000 = ( 4.06 / 4 ) ^ 4t

8/5 = ( 203/200 ) ^ 4t

b = aᶜ ⇔ logₐb = c

The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

The given parameters are:

Perimeter = 210 meters

Let the length parallel to the wall be represented as z and the width be x

So, the perimeter of the fence is

P = 2x + z

This gives

210 = 2x + z

Make x the subject

x = 1/2(210 - z)

The area of the wall is calculated as

A = xz

So, we have

A = 1/2(210 - z) * z

This gives

A = z/2(210 - z)

Rewrite as

A(z) = z/2(210 - z)

Hence, the function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

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The length of Marisa's garden is 10

The given parameters are:

Perimeter = 32 feet

Width = 6 feet

The perimeter is calculated as:'

Perimeter = 2 * (Length + width)

So, we have

2 * (Length + 6) = 32

Divide by 2

Length + 6 = 16

Subtract

Length = 10

Hence, the length of Marisa's garden is 10

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The required Proxima Centauri is approximately 24.9 trillion miles away from the Sun.

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a mile, for liquid we have liters, and so on.

Proxima Centauri is a star located in the Alpha Centauri star system and is approximately 4.24 light years away from the Sun.

To convert light years to miles, we can use the conversion factor of approximately 5.88 trillion miles per light year. So, the distance of Proxima Centauri from the Sun in miles can be calculated as:

= 4.24 light-years × 5.88 trillion miles/light year
= 24.9 trillion miles

Thus, Proxima Centauri is approximately 24.9 trillion miles away from the Sun.

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