A cylinder has a cross-sectional area of 17m² and a length of 14 m what is the volume of the cylinder

The smallest possible area of the new rectangle is 52 square units.

In the question, we are given that a rectangle has side lengths of integral value.

We assume the lengths to be x and y units respectively, such that x and y are integers.

In the new arrangement, one pair is increased by 30%, and the other pair is decreased by 20%, such that the new sides are also integers.

We assume a 30% increase in x.

New side = x + 30% of x = x + 30/100 of x = x + 3x/10 = 13x/10.

For this to be an integer, x needs to be a multiple of 10.

Since we are considering the smallest area, we will consider the smallest multiple of 10, that is, 10 itself.

Hence, side 1 = 13 units.

We assume a 20% decrease in y.

New side = y - 20% of y = y - 20/100 of y = y - y/5 = 4x/5.

For this to be an integer, y needs to be a multiple of 5.

Since we are considering the smallest area, we will consider the smallest multiple of 5, that is, 5 itself.

Hence, side 2 = 4 units.

Now, the area of this rectangle is the product of its sides = 13*4 sq. units = 52 sq. units.

Therefore, the smallest possible area of the new rectangle is 52 square units.

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Answer: 48 and 12.

Step-by-step explanation:

Let the smaller number is x. Hence, the larger number is 4*x.

The difference between 2 number is 36.

So,

4*x-x=36

3*x=36\ |:3

x=12.

4*x=12*4

4*x=48.

Good luck an' have a nice day!

The length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

By intersecting chords theorem:

QM×QL = QJ×PQ

10×8 = QJ(QJ/4)

4×80 = QJ²

QJ = 4√20 units

Thus, the length of QJ is 4√20 units if the QJ = 4×PQ after using the intersecting chords theorem.

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The pair of equations that has (0, 8) as its solution is: A. equation A and equation C.

The solution to a system of linear equations that are graphed is the pair of x and y coordinates of the points where two lines intersect.

In the graph given, the lines representing equations A and C intersect at point (0, 8). Therefore, the pair of equation that has a solution of (0, 8) is: A. equation A and equation C.

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Answer:

The expression is 42-17-19 OR 42-(17+19).

Step-by-step explanation:

First, we can indicate that we can use subtraction because is giving them away for his birthday.

"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".

That represents taking away 17 and 19 means that it is subtracting them.

Hope this helps. (:

Answer:

x ≈ 6.5 , y ≈ 12.1

Step-by-step explanation:

(2x)² + (10.2)² = (16.5)²

4x² = 272.25 - 104.04

x² = 168.21 ÷ 4

x = √(42.0525) ≈ 6.5

y² = 42.0525 + 104.04 = 146.0925

y = √(146.0925) ≈ 12.1

The ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)

The ordered pairs are given as:

(-5, -3), (-4, -4), (-2, 2), (1, 3), (1, -2), (2, 1), (5, -4)

For a set of ordered pairs to represent a function, each x value must point to exactly one y value

From the above ordered pairs, we have:

(1, 3) and (1, -2)

The x value 1 has y values 3 and -2

When one of these pairs is removed, the graph becomes a function

Hence, the ordered pair that can be removed so that the resulting graph represents a function is (1, 3) or (1, -2)

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The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).

It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.

On this note, given that the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).

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Options 1, 3 and 5. The true statements based on the fact that c and d are parallel are:

The sum of the angles m<4 + m<3 = 180

m<4 + 82 = 180

m<4 = 180 - 82= 98

From the question we have the first as alternate interior angles. The second is corresponding angles and the last option is vertical angles.

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Answer:

Step-by-step explanation:

The graph which is the best interpretation of the table given is; On a coordinate plane, the x-axis is labeled Quantity and the y-axis is labeled price. Points are at (1, 2), (2, 3.5), (3, 5), (4, 6.5), (5, 8), (6, 9).

The table given in the task content is a tabular representation of the quantity and the corresponding prices. On this note, plotting the quantity on the x-axis and the price on the y-intercept with the point descriptions above best represents the graph of the table.

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Answer:

The short answer to my well taught friend, is A

(4x + 5)(3x + 10) or 12x² + 55x +50

Forming the Expression for the Area of Rectangle

The formula for the area of a rectangle is given as,

Area, A = length × breadth

Here, the dimensions of the rectangle are given as,

length = (4x + 5)

breadth = (3x + 10)

∴ The equation for the area of the rectangle is,

A = (4x + 5)(3x + 10)

A = 12x² + 55x +50

Hence, 12x² + 55x +50 is the required expression.

Degree and Classification of the Expression

The highest power of a variable that is present in an expression is known as its degree.

Since the degree of the expression formed in part a is 2, it is classified to be a quadratic expression.

Closure Property For Polynomials

When the output is the same kind of object as the inputs, an expression is said to be closed. The expression obtained for the area of the rectangle is a combination of constants and variables closed under multiplication and addition.

Hence the expression formed in part a indicates at the closure property for polynomials.

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Mark the point on the coordinate system and draw the polygon (attachment).

This is the trapezoid.

The formula of an area of a trapezoid:

[tex]A=\dfrac{a+b}{2}\cdot h[/tex]

a, b - the lengths of the parallel sides

h - the height

Substitute:

[tex]a=9,\ b=7,\ h=8\\\\A=\dfrac{9+7}{2}\cdot8=\dfrac{16}{2}\cdot8=8\cdot8=64[u^2][/tex]

[tex]\huge\boxed{A=64u^2}[/tex]

2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a segment bisector splits a segment into two congruent parts)

3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a segment bisector splits a segment into two congruent parts)

4) [tex]\angle AEB \cong \angle CED[/tex] (vertical angles are congruent)

5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)

6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)

7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)

8) [tex]\angle BEC \cong \angle AED[/tex] (vertical angles are congruent)

9) [tex]\triangle BEC \cong \triangle DEA[/tex] (SAS)

10) [tex]\angle ECB \cong \angle EAD[/tex] (CPCTC)

11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation/Question:}[/tex]

[tex]\mathbf{7n - (4n - 3)}[/tex]

[tex]\huge\textbf{Convert equation/question to:}[/tex]

[tex]\mathbf{= 7n - 1(4n - 3)}[/tex]

[tex]\huge\textbf{Solving the equation/question:}[/tex]

[tex]\mathbf{= 7n - 1(4n) - 1(-3)}[/tex]

[tex]\mathbf{= 7n - 4n + 3}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (7n - 4n) + 3}[/tex]

[tex]\mathbf{= 7n - 4n + 3}[/tex]

[tex]\mathbf{= 3n + 3}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{3n + 3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm f(x) = x^{3}+2x^{2}-5x-6[/tex]

The function is a cubic function and the graph of the cubic function will be a curve.

As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.

Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.

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Answer:

8125 x 10^-3

= 8.125

8125 g

= 8.125 kg

Step-by-step explanation:

First, note that g is the same as grams and kg is the same as kilograms. Thus, when you are asking to convert 8125 g to kg, you are asking to convert 8125 grams to kilograms.

A gram is smaller than a kilogram. Simply put, g is smaller than kg. In fact, a gram is "10 to the power of -3" smaller than a kilogram.

Since a gram is 10^-3 smaller than a kilogram, it means that the conversion factor for g to kg is 10^-3. Therefore, you can multiply 8125 g by 10^-3 to get 8125 g converted to kg.

Here is the answer with the math showing you how to convert 8125 g to kg by multiplying 8125 by the conversion factor of 10^-3.

Answer:

8.125kg and 8125g

Step-by-step explanation:

1kg=1000g

Answer:

25

Step-by-step explanation:

2x+2+5x+3=180

7x=175

x=24

The distance between points M and N according to the task content is; 9.8 meters.

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

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Answer: 9.8 meters

Step-by-step explanation:  Trust Me!! I got the answer correct on Edge.

Q:  What is the distance between points M and N?

A:  9.8 meters  

Inequalities help us to compare two unequal expressions. The algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given statement "fifteen more than n is at least 48" can be written in the form of an algebraic expression as,

n+15 ≥ 48

Solving the inequality,

n ≥ 48 - 15

n  ≥ 33

Hence, the algebraic expression for fifteen more than n is at least 48 is n+15 ≥ 48; n≥33. Thus, the correct option is C.

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The probability that the colour changes, while she is watching, is 1/7

Concept: Event probability = number of favorite results /Total number of results

It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3  seconds, and then red for 30 seconds.

This means that the traffic light passes through 63 seconds to complete one-time cycle.

It is also given that Leah chooses a random 3 second time interval to watch the light.

We should find the probability that the color changes while Leah is looking.

The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.

Now let time t=0

The light changes at three different times: t=30,t = 33 and t = 63

This means that the light will change if Leah watches at intervals [27,30]

, [30,33] or [60,63]

Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.

That makes a total of 9 seconds out of 63

⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds

=9/63=17

∴ The probability that Leah observes the color change is 1/7

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[tex] \: \: \: \: \: \: \: \: \: \: \: \large\underline{\bf{ANSWER}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \tt↠(y^2+6)(−2y^2+7)[/tex]

[tex]\tt↠(-2y^2+7)y^2+6(-2y^2+7)[/tex]

[tex]\tt↠-2y^4+7y^2+6(−2y^2+7)[/tex]

[tex]\tt↠-2y^4+7y^2-12y^2+42[/tex]

[tex]\tt↠-2y^4-5y²+42[/tex]

Answer:

-2y⁴ - 5y² + 42

Step-by-step explanation:

[tex](y^2 + 6)(-2y^2 + 7)[/tex]

[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]

Here First terms are
[tex]y^2 \textrm{ and } -2y^2\\(y^2)(-2y^2) = -2y^4[/tex]

Outer terms are y² and 7 ==>  (y²)(7) = 7y²

Inner terms are 6 and -2y² ==> 6(-2y²) = -12y²

Last terms are 6 and 7 ==> 6.7 = 42

So result is obtained by adding all these terms

-2y⁴ + 7y² - 12² + 42 ==> -2y⁴ - 5y² + 42

Answer:

the graph is symmetric about the line y=-1

Step-by-step explanation:

A function is symmetric about y=a when the following is true for all points: f(a-x) = f(a+x). By just looking at the graph, it appears to be symmetric about y=-1, and it can be further proven, by finding the difference of two points, that have the same y-value. So for example if you look at (0, 1) and (-2, 1). The difference between 0 and -1 is 1, and the difference between -2 and -1, is also 1. And this appears to be true for all the other values as well. So the graph is symmetric about the line y=-1

Answer:

The graph is symmetric about the line x=-1

Step-by-step explanation:

Answer: -23

Step-by-step explanation:

-5-2x-2y

-5-2(3)-2(6)

-5-6-12 = -23

As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.

Note that  2,3,5 and 7   are the smallest primes, then use the reasoning from

(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.

But no such integers  k, l, m, and n  exist such that (k + 1)(l + 1)(m + 1) (n + 1)  = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors

Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents,  that, when 1 is added to each and all are multiplied together, would equal 20.  Put another way, we are looking for k, l and m ≥ 1   such that (k + 1)(l + 1)(m + 1) = 20

Note that the  only possibility here  is when we have 2 *2 *5  = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) =  2^4 * 3 * 5 = 240

Now......the only remaining possibility is  that this number is composed of the two smallest primes, 2 and 3,  and we are looking for  some k  and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities  are when k = 4 and l = 5, or vice-versa

So this number would factor as either 2^3 * 3^4   = 648  or 2^4 * 3^3 = 432 and both are > 240.

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Answer:

Step-by-step explanation:

exterior angle of a polygon = 360° ÷ number of sides

Answer:

2511

Step-by-step explanation: