Q1. Which of the following are well-defined sets?
(a) All the colors in the rainbow.

(b) All the points that lie on a straight line.

(c) All the honest members in the family.

(d) All the consonants of the English alphabet.

(e) All the tall boys of the school.

(f) All the efficient doctors of the hospital.

(g) All the hardworking teachers in a school.

(h) All the prime numbers less than 100.

(i) All the letters in the word GEOMETRY.

Answer: E. 384ft.

Step-by-step explanation:

112 - 16 = 96

96 x 4 = 384 ft.

Hopefully this helps! :)

Answer:

$15

Step-by-step explanation:

370-40=330

12+10=22

330÷22=15

15*22=330

The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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Amount of food in feeder at end is (16 - a) fl oz

Given that;

Amount of food in feeder in starting = 16 fl oz

Find:

Amount of food in feeder at end

Computation:

Assume;

a fl oz eats by animals

So,

Amount of food in feeder at end = 16 - a

Amount of food in feeder at end = (16 - a) fl oz

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Answer:

A C and D are not polynomial

Answer:

m = -2

Step-by-step explanation:

because of rise/run you can simply see the slope

The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

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Answer:

1/3

Step-by-step explanation:

\(g(f(x))=x \\ \\ g'(f(x))f'(x)=1 \\ \\ g'(f(x))=\frac{1}{f'(x)} \\ \\ g'(f(x))=\frac{1}{\cos x+2} \\ \\ g'(f(0))=\frac{1}{\cos(0)+2} \\ \\ g'(1)=\frac{1}{3}\)

Given:

The graph of a function.

To find:

The vertex form of the function.

Solution:

The graph is a U-shaped curve or a parabola with vertex at \((-3,-1)\).

The parent function for vertical parabolas is \(f(x)=x^2\) with vertex at (0,0).

It means the graph of \(f(x)=x^2\)  translated 3 units left and 1 unit down the get the given graph.

The vertex form of a parabola is:

\(y=a(x-h)^2+k\)

Where, a is a constant and (h,k) is vertex.

The vertex of the given parabola is at \((-3,-1)\). So, \(h=-3,k=-1.\).

\(y=a(x-(-3))^2+(-1)\)

\(y=a(x+3)^2-1\)            ...(i)

The graph passes through point (-2,0). Putting \(x=-2,y=0\), we get

\(0=a(-2+3)^2-1\)

\(1=a(1)^2\)

\(1=a\)

Putting \(a=1\) in (i).

\(y=1(x+3)^2-1\)

\(y=(x+3)^2-1\)

Therefore, the vertex form of the given graph is \(y=(x+3)^2-1\).

Answer:

3:2

Step-by-step explanation:

divide both numbers by 6

Answer:

10

Step-by-step explanation:

*+2=1

Answer:

The answer to your question is 10

Answer:

y= -1/6z + 6

Step-by-step explanation:

to turn 6 into a perpendicular

Answer:

the missing area is 10

Step-by-step explanation:

you can solve this by using pythagorean therom

Answer:

c = 14

Step-by-step explanation:

hope this helps

Answer:

10.0

Step-by-step explanation: 464:46

Answer:

no

Step-by-step explanation:

True, when nesting loops, the inner loop must be completely contained within the outer loop and must use a different control variable.

When nesting loops, one loop is placed inside another loop. The purpose of nesting loops is to execute a set of instructions repeatedly in a structured manner. In this context, the statement is true: the inner loop must be entirely contained within the outer loop, and a different control variable must be used for each loop.

By containing the inner loop within the outer loop, we ensure that the inner loop executes its iterations every time the outer loop iterates. This nested structure allows for more complex and detailed looping patterns.

Using different control variables for the inner and outer loops is necessary to maintain independent control over their iterations. Each loop should have its own variable to track and control its progress. This distinction is crucial in preventing conflicts and ensuring that the loops function as intended.

Therefore, when nesting loops, it is essential to follow these guidelines: the inner loop must be entirely contained within the outer loop, and a distinct control variable should be used for each loop to ensure proper execution and avoid potential errors.

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Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Answer:17

Step-by-step explanation:

|-3|^3 + 8

3^3 +8

9+8

17

Answer:

\(y = -\frac{2}{3}x + 490\)

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

y-intercept = \(490\)

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

\(\boxed{y = mx + c}\),

where:

m = slope,

c = y-intercept.

• We are given the equation:

\(2x + 3y = 1470\)

To change this into the slope-intercept form, we must make y the subject:

\(3y = -2x + 1470\)          [subtract \(2x\) from both sides]

⇒ \(y = -\frac{2}{3}x + \frac{1479}{3}\)        [divide both sides by 3]

⇒ \(y = -\frac{2}{3}x + 490\)

• Comparing this equation with the general form equation, we see that:

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

c = \(490\).

This means that the gradient is \(\bf -\frac{2}{3}\), and the y-intercept is \(\bf 490\).

Answer:

Step-by-step explanation:

Given the equation of the lines 3x + y - 4 = 0, 4x - 5y + 30 = 0,  y = – 3x – 1, and - 4x + 5y + 10 = 0. For us to be able to predict the type of quadrilateral formed by this lines, we need to find the slope of each of the lines. Any two lines with the same slope will be parallel lines.

The standard form of equation of a line is expressed as y = mx+c where m is the slope of the line.

Re-writing each equation in standard format:

For the line 3x + y - 4 = 0;

3x+y = 4

y = 4-3x

y = -3x + 4

Hence the slope of the line is -3

For the line 4x - 5y + 30 = 0:

4x-5y = -30

-5y = -30-4x

-5y = -4x-30

divide through by -5

y = 4/5 x + 6

Hence the slope of this line is 4/5

For the line y = – 3x – 1:

The line is already in its standard format, hence the slope of the line is -3

For the line - 4x + 5y + 10 = 0:

-4x+5y = -10

5y = -10+4x

5y = 4x-10

divide through by 5

y = 4/5 x - 10/5

y = 4/5 x - 2

Hence the slope of this line is 4/5

From the slopes above, it can be seen that the line 4x - 5y + 30 = 0 is parallel to  - 4x + 5y + 10 = 0 and that of the line 3x + y - 4 = 0 is parallel to y = – 3x – 1 due to their similar slope.

To know the the type of quadrilateral formed by this lines, first we need to check whether two dissimilar lines are perpendicular to each other. If they are perpendicular to each other, it means the quadrilateral could be a square or a rectangle but if otherwise, it will either be a parallelogram or a rhombus.

For two lines to be perpendicular, the product of their slope must be -1 i.e m1m2 = -1

For the first two lines:

m1 = -3 and m2 = 4/5

Taking their product:

-3*4/5 = -12/5

Since the product did not give use -1, hence the quadrilateral is neither a square nor a rectangle. The quadrilateral can therefore either be a parallelogram or a rhombus since the intersecting lines of either shapes are not perpendicular to each other.

Yes, it is possible to find the volume of the tent. The volume of the tent is 84 cubic feet.

What is triangular prism?

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Given that the total surface area of a triangular prism is 136 square feet. The area of tent excluded the area of the bases is 112 square feet.

Then the surface area of the bases is (136 - 112) = 24  square feet.

The surface area of one base is 24/2 = 12 square feet.

The height of the tent is 7 feet.

The volume of a triangular prism is

1/2 bhl

= surface area of base × height

= 12 × 7

= 84 cubic feet.

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Answer:

\((1)\;\;\;\text{Slope }= \dfrac{3}{5}\\\)

(2) Equation of line in slope-intercept form is
\(y = \dfrac{3}{5}x + 3\)

(3) Equation of line in standard form is:
\(5y - 3x = 15\)

Step-by-step explanation:

Equation of a line in slope-intercept form is
y = mx + b

where m = slope and b = y-intercept

Slope = \(\dfrac{y2 - y1}{x2-x1}\)

where (x1, y1) and (x2, y2) are two points on the line.

y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run

We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.

So we get one of the points (-5, 0)

We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0

So another point on the line is (0, 3)

Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3

run = x2 - x1 = 0 - (-5) = 0+5 = 5

\((1)\;\;\;\text{Slope = $\dfrac{3}{5}$}\)

(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3

So equation of line in slope-intercept form is
\(y = \dfrac{3}{5}x + 3\)

(3) Equation in standard form
In (2) subtract (3/5)x from both sides.

\(y - \dfrac{3}{5}x = 3\)

We can multiply both sides by 5 to get
\(5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15\)

The parametric equations for the curve are:

x = -5t^3 - 3t

y = t

To find parametric equations for the curve x = -5y^3 - 3y, we can set y as the parameter and express x in terms of y.

Let y = t, where t is the parameter.

Substituting y = t into the equation x = -5y^3 - 3y:

x = -5(t^3) - 3t

The interval for the parameter values depends on the context or specific requirements of the problem. If no specific interval is given, we can assume a wide range of values for t, such as all real numbers.

So, the correct answer is:

A. x = -5t^3 - 3t, y = t

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Let f be the function given by f (x) = e + cos x - 1. the value of f' (2)  is 0.0349

The given function is f (x) = e + cos x - 1,

f' is the derivative of the given function, and the derivative is sort for below

f (x) = e + cos x - 1

f' (x) = 0 + -sin x - 0

f' (x) = -sin x

for f' (2) we substitute the x = 2 in the derivative

f' (x) = -sin x

f' (2) = -sin 2

f' (2) = -sin 2

f' (2) = -0.0349

hence f' (2) = -0.0349

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