What is the solution to the system of equations?

Answer:

3 and 5/83

Step-by-step explanation:

I believe that the answer is 21.48

The factory would need approximately a circumference of 21.98 feet of the braid to go all the way around the outside of the circular rug.

We have,

The formula for the circumference (C) of a circle is:

C = 2πr

where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

In this case, the radius of the rug is 3.5 feet, so we can calculate the circumference as:

C = 2 × 3.14 × 3.5 = 21.98 feet

Therefore,

The factory would need approximately a circumference of 21.98 feet of the braid to go all the way around the outside of the circular rug.

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The statement "The two-second rule is the accepted method of computing the following distance" is true.

The two-second rule is a widely recognized guideline used to determine a safe distance to maintain between vehicles while driving. It suggests that drivers should keep a time gap of at least two seconds between their vehicle and the vehicle in front of them.

The two-second rule is based on the principle that it takes about two seconds for a driver to perceive a hazard, react to it, and begin to apply the brakes. By maintaining this time gap, drivers allow themselves enough space to react to sudden changes in the traffic situation or unexpected maneuvers by the vehicle ahead.

Thus, the given statement is true.

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Answer:

v=7

Step-by-step explanation:

my previous answer was incorrect, my bad

Answer: v=-7

Step-by-step explanation:

3(23−2v)+3v=48

Distribute:

69-6v+3v=48

Combine like terms:

-6v+3v=-3v

69-3v=48

Subtract 69 on both sides:

69-69-3v=48-69

-3v=-21

Divide 3 on both sides:

-3v/3=-21/3

v=-7

Answer: 10.8 seconds

Step-by-step explanation:

\(-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)\)

Answer:

(0, 2)

Step-by-step explanation:

The solution to the system based on the graph is (0, 2)

Reason: Lines are intersecting at point (0, 2) which satisfy the given equations.

Step-by-step explanation:

12 + 3=15

48+ 3=51

10 + 3=13

40 + 3=43

12 + 3=15

48 + 3=51

10 + 3=13

40+ 3=43

Answer:

y = 2x + 54

Step-by-step explanation:

slope of equation:

(y2-y1)/(x2-x1)

= (72-58)/(9-2)

= 14/7

= 2

y = 2x + b

58 = 2(2) + b

58 = 4 + b

b = 54

The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:

Step 1 - Introduce the trigonometric equation:

cos 2x - cos x = - 1

Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:

cos² x - sin ² x - cos x = - 1

Step 3 - Use fundamental trigonometric formula:

cos² x - 1 + cos² x - cos x = - 1

2 · cos² x - cos x = 0

Step 4 - Use algebra properties to factor the expression:

cos x · (2 · cos x - 1) = 0

Step 5 - Find the solutions of the expression:

cos x = 0 → x = {π / 2, 3π / 2}

2 · cos x - 1 = 0

2 · cos x = 1

cos x = 1 / 2 → x = {π / 3, 5π / 3}

The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

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The approximate length of arc is 2.2

We can find the approximate length of arc s on the circle given below by using the formula given below:

arc length = θ/360° × 2πr Where,θ = central angle of the arc in degrees r = radius of the circle

Given that, radius of the circle = 5.6 in and central angle of the arc is 75°.

Therefore, the approximate length of arc s on the circle is as follows:

arc length = θ/360° × 2πr

arc length = 75/360° × 2 × 3.14 × 5.6

arc length = 0.208 × 2 × 3.14 × 5.6

arc length = 2.19 (rounded to nearest tenth)

Therefore, the approximate length of arc s on the circle is 2.2 in.

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Answer:

CENTROID

Step-by-step explanation:

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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H ;-)

x = -3 and y = -2

2x² - 5xy - y³ =

= 2 · (-3)² - 5 · (-3) · (-2) - (-2)³ =

= 2 · 9 - 30 - (-8) = 18 - 30 + 8 =

= -12 + 8 = -4

Answer:

\(2 {x}^{2} - 5xy - {y}^{3} \\ x = - 3 \\ y = - 2 \\ 2 { (- 3)}^{2} - 5 \times - 3 \times - 2 - { (- 2)}^{3} \\ 2 \times 9 + - 30 - - 8 \\ = 18 - 30 + 8 \\ = - 4 \\ thank \: you\)

lim (x → a) f(x) = ∞ , The limit does not exist and is neither ∞ nor - ∞

The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x. If for a particular x, and y values are coming it means it is not a function. If it crosses y-axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function

From the graph, we know that limit at point a is:

lim (x→a) f(x) exists if and only if

lim (x →a⁺) f(x) = lim (x→a⁻) f(x) and ≠ ∞

∴ right hand side limit = left hand side limit

lim (x →a⁺) f(x) = - ∞

lim (x →a⁻) f(x) = - ∞

∴ lim (x → a) f(x) = ∞

thus, option B is the correct answer.

The limit does not exist and is neither ∞ nor - ∞

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Answer:

1. \(\frac{1}{9}\)

4. \(\frac{3^{-4} }{3^{-2} }\)

Step-by-step explanation:

Answer:

I think 9 but dont quote me on it

Answer:

2

Step-by-step explanation:

in khan academy i put 9 because thats what the last person said here but it was wrong and the correct answer was 2 so its 2 for sure.

Answer: The area, in square feet, of the piece of wood is \(32 ft^{2}\).

Step-by-step explanation:

Give: Length = 8 feet

Width = \(\frac{1}{2} \times 8\) = 4 feet

As piece of wood is similar to that of a rectangle. Hence, formula to calculate area is as follows.

\(Area = length \times width\)

Substitute the values into above formula as follows.

\(Area = length \times width\\= 8 feet \times 4 feet\\= 32 ft^{2}\)

Thus, we can conclude that the area, in square feet, of the piece of wood is \(32 ft^{2}\).

Answer:

(5+5+5+5)*5

20*5=100

\(5\cdot5\cdot5-5\cdot5=125-25=100\)

Using the relation between velocity, distance and time, it is found that she traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

Velocity is distance divided by time, that is:

v = d/t.

For the first part, we have that she cycled a distance of d m in t seconds, at a velocity of 10 m/s, hence:

10 = d/t

d = 10t.

For the second part, we have that she cycled a distance of 500 - d meters, in 22 - t seconds, at a velocity of 50 m/s, hence:

50 = (500 - d)/(22 - t).

Since d = 10t, and applying cross multiplication:

500 - 10t = 50(22 - t)

500 - 10t = 1100 - 50t

40t = 600

t = 600/40

t = 15.

22 - t = 22 - 15 = 7, hence:

She traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

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The number in the solution set is 20

From the question, we have the following parameters that can be used in our computation:

x + 30 = 50

To find the solution to the equation x + 30 = 50, we can start by isolating x on one side of the equation:

x + 30 = 50

Subtracting 30 from both sides, we get:

x = 50 - 30

Simplifying, we get:

x = 20

Hence, the only number that belongs to the solution set of the equation x + 30 = 50 is 20.

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Answer:

Step-by-step explanation:

YES IS THE ANSWER BECAUSE X=9

AND 11+3=87

Answer:

5p+7q................

Katelyn needs to mow 3 lawns to have enough money to buy the skateboard.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' be the no. of lawns she has to mow.

Given, Katelyn wants to buy a $75.00 skateboard and she has $25.00 saved and she mows lawns to make extra money and earns $20.00 for each lawn he mows.

Therefore the inequality that represents this context is,

20x + 25 ≥ 75.

20x ≥ 75 - 20.

20x ≥ 55.

x ≥ 55/20.

x ≥ 2.75, But she has to mow a lawn completely to get paid so she must mow 3 lawns.

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Answer:

3 lawns

Step-by-step explanation:

25 is what she haves now

3x20(how much she gets paid)=60

25+60=85

85-75=10 (she has 10 dollars left after she buys the skateboard

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

Given that,

f(x) = 1 + |2x - 5|

And,

f(x) = {f₁       x < a

         {f₂      x ≥ a

Now,

We have,

f(x) = 1 + |2x - 5|

And,

By definition of absolute value,

|x| = {x        x ≥ 0

       {-x       x < 0

And,

Given the absolute value,

|2x - 5|

Solve for x,

i.e.

2x - 5 = 0

We get,

x = 5/2 = 2.5

i.e.

a = 5/2

i.e.

For all values greater than x = 5/2, 2x - 5 is positive,

And,

For all values less than x = 5/2, 2x - 5 is negative.

So,

|x| = {x        x ≥ 5/2

       {-x       x < 5/2

i.e.

|2x - 5| = {2x - 5        x ≥ 5/2

              {-(2x - 5)       x < 5/2

Now,

f(1) = 1 + |2(1) - 5|

We get,

f₁ = 4

And,

f(2) = 1 + |2(2) - 5|

We get,

f₂ = 2

Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

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The smallest of the two integers is 61

Represent the consecutive numbers with x and y, where x is the smallest of the two numbers.

So, we have the following system of equations

x + y =123

y = x + 1

Substitute x + 1 for x in x + y =123

x + x + 1 =123

Subtract 1 from both sides

x + x =122

Evaluate the like terms

2x = 122

Divide both sides by 2

x = 61

Hence, the smallest of the two integers is 61

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Answer:

D. The m<4 is 137°

\( < 4 = 180 \degree - 43 \degree \\ < 4 = 137 \degree\)

Answer

Explanation

The equation in slope-intercept form is:

where m is the slope and b is the y-intercept.

Additionally, the slope m can be calculated using the change between two points as it is a line and will be the same in all points:

Considering the two points given, we can assume that point one is (-2, -5) and point two is (-5, -8). Replacing these values we get:

Simplifying:

Then, replacing the slope calculated in the equation we get:

Next, we have to choose one of the given points to replace in the equation and solve for b. For example, choosing (-2,-5):

Finally, our equation is:

The value of x is given as follows:

x = 2.25.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

From the image at the end of the answer, we have that 3 is the geometric mean of 4 and x, hence the value of x is obtained as follows:

4x = 3²

4x = 9

x = 9/4

x = 2.25.

The image is given at the end of the answer.

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