For the following exercises, solve each system by elimination. 4x + 6y + 9z = 0 . -5x + 2y-6z = 3 7x-4y + 3z = -3 =

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

The maximum value of Z is 1584.

The given linear programming problem can be solved using the graphical method.

Here are the steps to solve the given linear programming problem using the graphical method.

Step 1: Convert the given inequalities into equations.

5x + 3y = 45

8 = x

10 = y

Step 2: Plot the line 5x + 3y = 45 and shade the region above it as it is infeasible for the given conditions.

Step 3: Plot the lines x = 8 and y = 10 and shade the region below them as they are limiting conditions.

Step 4: Check the intersection point of the two limiting lines x = 8 and y = 10. The intersection point is (8, 10).

Step 5: Mark any point above the line 5x + 3y = 45, for example, (0, 15).

Step 6: Draw a line from (0, 15) to (8, 10).

The line intersects the line 5x + 3y = 45 at (9, 12).

Step 7: The maximum value of Z = 80x + 72y at point (9, 12) is given by:

Z = 80 × 9 + 72 × 12

= 720 + 864

= 1584

Therefore, the maximum value of Z is 1584.

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The daily production number that yields a minimum cost is 20 units, and the minimum cost is 600.

The manufacturer of lighting fixtures has daily production costs of

C = 800 - 10x + 0.25x²

where C is the total cost (in dollars) and x is the number of units produced. To determine the daily production number that yields the minimum cost, let us find the first derivative of C with respect to

x.

dy/dx

= -10 + 0.5xSetting Dy/dx = 0,

we get:

-10 + 0.5x

= 0⟹ 0.5x

= 10

⟹ x

= 20

Therefore, when 20 units of the product are produced, the total cost is minimized. Next, to find the minimum cost, we substitute the value of x = 20 into the expression for C.

C = 800 - 10(20) + 0.25(20²)

C = 600.

So, when 20 units of the product are produced, the minimum cost is 600.

The daily production number that yields a minimum cost is 20 units, and the minimum cost is 600.

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Step-by-step explanation:

The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.

Answer:

Yeah, √(25) is 5.

Step-by-step explanation:

Given problem,

→ √(25) = 5

Checking the equation,

→ √(25) = 5

→ 25 = (5)²

→ 25 = 25

→ LHS = RHS

Thus, equation is proved.

When the parallel lines are cut by a transversal, the values for the measurement of ∠5 and ∠7 is 99° each.

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

In the given diagram the parallel lines are cut by a transversal.

The measure of angle 4 is, m∠4 = 81°.

It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.

So, m∠4 + m∠5 = 180°

81° + m∠5 = 180°

m∠5 = 180° - 81°

m∠5 = 99°

Now, as it can be seen in the image ∠5 and ∠7 are vertically opposite angles.

So, they will be congruent or equal to each other.

So, it is obtained that -

m∠5 = m∠7

m∠7 = 99°

Therefore, the measures of angles are m∠5 = 99° and m∠7 = 99°.

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Answer:

Hey there the correct answer to your question will be below.

Step-by-step explanation:

Work: 300/68 x 60 will give you 264.7 which will round to 265*

1/68 x 3,600 will be 52.94 and if you round that you will get 53*

So the answer will be

ABOUT: 265 words per minute

ABOUT: 53 in one hour

EXACT: 264.7 words per minute

EXACT: 52.94 in one hour

Hope this helps!

By: xBrainly

To calculate the moment of inertia of an object, you need to know its mass and the distance it is from the axis of rotation. In this case, the object has a mass of 12 kg and is distributed 4 meters from the axis of rotation. The formula to calculate the moment of inertia is I = mr^2, where the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

Using this formula, we can calculate the moment of inertia of the object:

I = 12 kg x (4 m)^2

I = 192 kgm^2

Therefore, the moment of inertia of the object is 192 kgm^2.
To calculate the moment of inertia for an object, you can use the following formula:

Moment of Inertia (I) = Mass (m) × Distance² (r²)

Given the object's mass is 12 kg and the mass is distributed 4 meters from the axis of rotation, we can plug these values into the formula:

I = 12 kg × (4 m)²

Now, we'll square the distance:

I = 12 kg × 16 m²

Finally, multiply the mass and the squared distance:

I = 192 kg·m²

So, the moment of inertia of the object is 192 kg·m².

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The required length of the rectangle is 89 m.

Given that,
The area of a rectangular field is 6942 m. If the width of the field is 78 m, what is its length is to be determined.

Perimeter is the measure of the figure on its circumference.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

The area of the rectangle = length * width
                                6942  = length * 78
                                length = 89 m

Thus, the required length of the rectangle is 89 m.

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Answer:

Check all of them

Step-by-step explanation:

If you are on Edg, just check all of them.

The value of the radius is √2 units

To do this, we start by calculating the distance between the opposite vertices of the square.

The opposite vertices are:

(1, 2) and (-1, 4)

The distance between these vertices is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(1 + 1)² + (2 - 4)²

Evaluate

d = √8

Evaluate the exponent

d = 2√2

Divide this distance by 2 to determine the radius

Radius = 2√2/2

Evaluate

Radius = √2

Hence, the value of the radius is √2 units

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Answer:

32 m^2

Step-by-step explanation:

First find the real dimensions of the dining hall

The scale factor is 4m /3 cm

6 cm * 4m / 3cm = 8 m

3 cm *  4m / 3cm = 4 m

The area of the dining hall is

A = l*w

A = 8m * 4m = 32 m^2

The area under the probability density function to the left of the mean for the standard normal distribution is 0.5.

The standard normal distribution, also known as the Z-distribution, is a bell-shaped distribution with a mean of zero and a standard deviation of one. The area under the curve of a probability density function represents the probability of an event occurring. Since the mean of the standard normal distribution is at the center of the distribution, the area to the left of the mean is symmetrically equal to the area to the right of the mean. Therefore, the area under the probability density function to the left of the mean is 0.5 or 50%. This means that there is a 50% probability of observing a value less than the mean in a standard normal distribution.

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Riboflavin is similar to thiamin in that option d: both riboflavin and thiamin serve as coenzymes in energy metabolism.

Riboflavin is similar to thiamin in that both serve as coenzymes in energy metabolism. Coenzymes are molecules that assist enzymes in carrying out their biological functions. In the case of riboflavin and thiamin, they play vital roles in the conversion of carbohydrates, fats, and proteins into usable energy for the body.

Riboflavin, also known as vitamin B2, is an essential nutrient found in various foods such as dairy products, meat, eggs, and leafy green vegetables. It is a water-soluble vitamin, meaning it dissolves in water and is not stored in the body to a significant extent. Therefore, it needs to be regularly replenished through the diet.

Thiamin, also called vitamin B1, is another water-soluble vitamin that plays a crucial role in energy metabolism. It is involved in converting glucose into energy and is found in foods like whole grains, legumes, nuts, and seeds.

Both riboflavin and thiamin work as coenzymes by participating in specific enzymatic reactions. They assist enzymes in catalyzing chemical reactions necessary for energy production. Riboflavin, in the form of its coenzyme derivatives flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN), acts as a carrier of hydrogen atoms in metabolic reactions. Thiamin, on the other hand, is converted into its active form, thiamin pyrophosphate (TPP), which plays a crucial role in the metabolism of carbohydrates.

Now, let's address the options mentioned in the question to understand how riboflavin is similar to thiamin:

a. both are easily destroyed by heat: While it is true that riboflavin and thiamin can be degraded by heat, riboflavin is more sensitive to heat than thiamin. Riboflavin is easily destroyed when exposed to high temperatures, such as during cooking or food processing. Thiamin, although also susceptible to heat, is relatively more stable.

b. both are easily destroyed by ultraviolet light: This statement is incorrect. Riboflavin is indeed sensitive to ultraviolet (UV) light, which is why it is often stored in opaque containers to protect it from light exposure. However, thiamin is not particularly affected by UV light.

c. though rare, both can be toxic when consumed in high amounts: While excessive intake of any nutrient can potentially be harmful, toxicity from riboflavin and thiamin is rare. These vitamins are considered safe for consumption in recommended amounts, and any excess is typically excreted in the urine.

d. both serve as coenzymes in energy metabolism: This statement is correct, as explained earlier. Both riboflavin and thiamin are essential coenzymes involved in energy metabolism.

e. both are found in abundant amounts in pork: While pork is a source of several nutrients, neither riboflavin nor thiamin is found in exceptionally high amounts in pork. Riboflavin is more commonly found in dairy products, while thiamin is abundant in whole grains and legumes.

In summary, the correct answer is option d: both riboflavin and thiamin serve as coenzymes in energy metabolism. They play important roles in converting food into energy and are essential for overall health and well-being.

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A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.

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

The car is 120 miles away when the motorcycle starts.

The bike gains on the car at 30 mph (70-40).

It takes 4 hours for the bike to close the gap (120/30).

In 4 hours, the bike and the car are 280 miles from the starting point.

---------

4*70 = 280

7*40 = 280

Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.

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the interquartile range of that plot is 10

q3 is 30 and q1 is 20 so you subtract 20 from 30 to get 10

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

ok so we organize it by:

9, 12, 13, 14, 14, 18, 19, 22, 22, 23, 42

so we eliminate 42 and so we cross out one from the left side and one from the right side and we repeat that and we find the center which is any number between 14-18

Part A :

Two numbers Hugh could spin to get a positive product is:

-4 and -3

Part B:

Two numbers Hugh could spin to get a negative product is:

5 and -6

Given, Hugh is playing a game.

He spins each spinner and then multiplies the numbers to find the product.

Part A:

An example of two numbers Hugh could spin to get a positive product is:

-4 from spinner A

and -3 from spinner B.

therefore, -4×-3 = 12

hence to negative numbers gives a positive product.

Part B:

An example of two numbers Hugh could spin to get a negative product is:

5 from spinner A

and -6 from spinner B.

therefore, 5×-6 = -30

hence one negative and one positive number, when multiplied gives a negative product.

Hence we get the required answers.

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The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

Specificity and memory are two crucial properties that determine adaptive immunity. Both specificity and memory pertain to the adaptive immune system's capacity to recognize and attack certain diseases, as well as to promptly react to pathogens to which it has already been exposed.

Adaptive immunity can offer an enduring defense, perhaps for the duration of a person's lifespan. In certain circumstances, such as with chickenpox, it does not confer permanent protection; for instance, a person who recovers from measles is now protected against measles for the rest of their life.

Specificity, diversity, specialization, memory, and self/non-self identification are the immunologic characteristics that define adaptive immunity, and these cells both create and show antigen-binding cell surface receptors.

The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

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For the polygon the individual value of the interior angles.

a) 15 sides is 145°

b) 20 sides is 108°

c) 3 sides is 60°

d) 4 sides is 90°

e) 100 sides is 18°

A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.

a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2180 / 15 = 145 degrees per angle.

b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2160 / 20 = 108 degrees per angle.

c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 180 / 3 = 60 degrees per angle.

d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 360 / 4 = 90 degrees per angle.

e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 1800 / 100 = 18 degrees per angle.

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The cost of both plans when the cost is the same will be $68.8.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's suppose the number of minutes is x

Now,

The total cost of plan A ⇒

25 + 0.14x

The total cost of plan b ⇒

9 + 0.19x

Now, if the total cost is the same

25 + 0.14x = 9 + 0.19x

0.19x - 0.14x = 25 - 9

0.05x = 16

x = 320

Hence "The cost of both plans when the cost is the same will be $68.8".

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The measures of angle ABC and DBC are 41 degrees and 43 degrees

The angles are given as

Angle ABC = (5x + 1) degrees

Angle DBC = (6x - 5) degrees

Angle ABD = 84 degrees

The angles add up to 84 degrees

So, we have:

ABC + DBC = 84

This gives

5x + 1 + 6x - 5 = 84

Evaluate the like terms

11x = 88

Divide both sides by 11

x = 8

Substitute x = 8 in Angle ABC = (5x + 1) degrees and Angle DBC = (6x - 5) degrees

Angle ABC = (5 x 8 + 1) degrees

Angle DBC = (6 x 8 - 5) degrees

Evaluate

Angle ABC = 41 degrees

Angle DBC = 43 degrees

Hence, the measures of angle ABC and DBC are 41 degrees and 43 degrees

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the values 17, 12, 24, 28, 23, 21, 5, 20, 18, 22, 6, the third level consists of the values 23, 21, 5, and 20.

A max heap is a complete binary tree where the value of each node is greater than or equal to the values of its children. In the given set of values, we can visualize the max heap as a binary tree structure. The root node is 28, followed by the second level containing the nodes 24 and 23. The third level, in a complete binary tree, starts with the left child of the second level node and continues to the right child. Thus, the third level consists of the values 23, 21, 5, and 20.

Note: It is important to understand that the levels in a binary tree are counted starting from 1, with the root node being at the first level.

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In this case, the p-value of .021 is greater than the alpha level of .01. Therefore, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the alternative hypothesis is true. The correct answer is D.

When conducting hypothesis testing, the a priori significance level (alpha) is set before the data is analyzed. This level is the threshold for determining whether the test statistic is significant or not. In this case, the alpha is set at .01, meaning that the probability of rejecting the null hypothesis when it is true is 1 in 100.

The test statistic is the calculated value that is used to determine whether the null hypothesis should be rejected or not. In this case, the test statistic has a p-value of .021. The p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed statistic, assuming the null hypothesis is true.

In other words, it tells us how likely it is that the observed data occurred by chance alone. To determine what to do next, we compare the p-value to the alpha level. If the p-value is less than or equal to the alpha level, then we reject the null hypothesis. If the p-value is greater than the alpha level, then we fail to reject the null hypothesis.

In this case, the p-value of .021 is greater than the alpha level of .01. Therefore, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the alternative hypothesis is true. It is important to note that failing to reject the null hypothesis does not mean that the null hypothesis is true, only that we do not have enough evidence to reject it.

There is no need to calculate the SEM (standard error of the mean) or accept the alternative hypothesis in this scenario. The correct answer is D, fail to reject the null hypothesis.

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To find the smallest positive solution to the equation $\sin(x) = \cos\left(2x \frac{\pi}{3}\right)$, we can rewrite it as $\sin(x) - \cos\left(2x \frac{\pi}{3}\right) = 0$.

Now, let's simplify the equation further. Using the identity $\cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right)$, we can rewrite the equation as $\sin(x) - \sin\left(\frac{2x \pi}{3} + \frac{\pi}{2}\right) = 0$. Applying the identity $\sin(\alpha) - \sin(\beta) = 2\cos\left(\frac{\alpha + \beta}{2}\right)\sin\left(\frac{\alpha - \beta}{2}\right)$, the equation becomes $2\cos\left(\frac{x - \frac{2x \pi}{3} - \frac{\pi}{2}}{2}\right)\sin\left(\frac{x + \frac{2x \pi}{3} + \frac{\pi}{2}}{2}\right) = 0$. Now we have two possibilities for the equation to hold: $\cos\left(\frac{x - \frac{2x \pi}{3} - \frac{\pi}{2}}{2}\right) = 0$ or $\sin\left(\frac{x + \frac{2x \pi}{3} + \frac{\pi}{2}}{2}\right) = 0$. For the first possibility, we have $\frac{x - \frac{2x \pi}{3} - \frac{\pi}{2}}{2} = \frac{\pi}{2} + n\pi$, where $n$ is an integer. Simplifying, we get $x = \frac{7\pi}{6} + 3n\pi$.

For the second possibility, we have $\frac{x + \frac{2x \pi}{3} + \frac{\pi}{2}}{2} = m\pi$, where $m$ is an integer. Simplifying, we get $x = \frac{6\pi}{7} + 3m\pi$. To find the smallest positive solution, we need to find the smallest positive value of $x$ that satisfies either of these equations. Evaluating the solutions, we find that the smallest positive solution is $x = \frac{6\pi}{7}$.

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Answer:

y=3x+2

Step-by-step explanation:

slope= rise/run

rise=3  run=1 slope=3

y intercept is 2

y=3x+2

Answer:

y = 3x + 2

Step-by-step explanation:

(1, 5) and (2, 8)

Slope:

m=(y2-y1)/(x2-x1)

m=(8-5)/(2-1)

m=3/1

m=3

y - y1 = m(x - x1)

y - 5 = 3(x - 1)

y - 5 = 3x - 3

y = 3x + 2

Step-by-step explanation:

Slope formula: \(\frac{y2}{x2} -\frac{y1}{x1} =m\)

m = slope

Take 2 points from the table.

(-3, 5) and (-2, 2).

Add these points to the formula:

\(\frac{2}{-2} -\frac{5}{-3} =\)

Solve:

\(\frac{2}{-2} -\frac{5}{-3} =\frac{-3}{1}\)

Option 1 is correct.

Y-intercept is where x = 0.

On the table, it's showing at x = 0, y = -4.

The y-intercept equals -4.

Answer:

A.

Step-by-step explanation:

Just find the lowest common multiple of 51 and 85.

51 = 3 * 17

85 = 5 * 17

3 * 5 * 17 = 255

The lowest common denominator for the fractions is 17.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

fraction = 8/51 and 19/ 85

Now, LCM of 51 and 85.

51 = 17 x 3

85= 17 x 5

So, the least common multiple is 17.

Hence, the lowest common denominator for the fractions is 17.

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Answer: a) b - 3

              b) 4b - 3

Step-by-step explanation:

b) b + 2b + b - 3

= 4b -3

Answer:

a)  b - 3

b)  4b - 3

Step-by-step explanation:

Mandy scores b points in a basketball game:

Jay scores 3 points less than Mandy:

Kareem scores 2 times as many points as Mandy:

Therefore, the number of points Jay scores in terms of b is b - 3.

To find the total number of points the three players score in terms of b, sum the three expressions:

⇒ b + (b - 3) + 2b

⇒ b + b - 3 + 2b

⇒ 2b - 3 + 2b

⇒ 4b - 3

Therefore the total number of points the three players score in terms of b is 4b - 3.

Answer:

x = -6 and y = -3

Step-by-step explanation:

x- 4y =6

x =4y +6......(i)

5x -4y =-18

20y +30 - 4y = -18

16y = -48

y = -3

x = -12+6

x = -6

The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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