Which statement is sometimes false?
J
K
The sum of a negative and a positive
number is a negative number.
The product of a negative and
a positive number is a negative
number.
L The quotient of a negative and
a positive number is a negative
number.
M
N
The sum of any two negative
numbers is a negative number.
The quotient of any two negative
numbers is a positive number.

The solution of the expression will be [ 26 / 8 ].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that 3 times as much as the sum of 3/4 and 2/6. The expression will be solved as below,

E = 3 [ ( 3/ 4) + ( 2 / 3 ) ]

E = 3 [ ( 18 + 8 ) / 24 ]

E = 3 x ( 26 ) / 24

E = 26 / 8

Therefore, the final solution for the expression is [ 26 / 8 ].

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The equivalent distance of 60,000 centimetres in kilometers as required to be determined is; 0.6 km.

According to the task content and the metric system conversions;

1 m = 100 cm

Therefore, it follows from proportion that; 60,000 cm is equivalent to; 60,000 / 100 = 600 m.

Additionally, it follows that; 1 km = 1000 m, it therefore follows from proportion that; 600 m is equivalent to; 600 / 1000 = 0.6 km.

Ultimately, the equivalent distance of 60,000 centimetres in kilometers is; 0.6 km.

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Slope of given line segment is 4/3.

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.

Given the coordinates of the two points that make up the line, we can use the slope of a line formula to determine the slope of the line directly. Slope = m = tan = (y2 - y1)/(x2 - x1) is the formula.

Slope of the line segment is rise / run

Slope = rise / run

From the graph, it is clear that rise = 12

run = 9

Slope = 12/9

Slope = 4/3

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The axis of symmetry of the given quadratic function is the vertical line x = -2. The correct answer would be an option (C).

A parabola is a U-shaped curve this is drawn for a quadratic function,

Determine the axis of symmetry of the quadratic function whose graph is y = - 2x² - 8x - 4.

The axis of symmetry of a parabolic function of the form y = ax² + bx + c is given by the formula x = -b/(2a).

In this case, a = -2, b = -8, and c = -4, so:

x = -(-8)/(2 × -2)

x = - 2

So, the axis of symmetry is the vertical line x = -2.

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The required solution to the given equation is x = 20. The correct answer would be an option (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

2(2x - 4) = 3(x + 4)

Apply the distributive property of multiplication,

4x - 8 = 3x + 12

Rearrange the likewise terms and apply the arithmetics operation,

4x - 3x = 12 + 8

x = 20

Thus, the required solution is x = 20.

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The equation x - 3y = -7 is a linear equation in slope-intercept form. To graph this equation, we can start by putting it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To do this, we can add 3y to both sides:

x = 3y - 7

To find the y-intercept, we can set x = 0 and solve for y:

0 = 3y - 7

3y = 7

y = 7/3

So the y-intercept of this line is (0, 7/3). To find the slope, we know that the coefficient of x is 1, so the slope is m = 1.

Now we can use the point-slope form of a linear equation to find three other points on the line:

y - 7/3 = 1(x - 0)

y = x + 7/3

We can find other three points by plugging in any value of x and solve for y:

(1, 4/3), (2,5/3), (3,6/3)

We can now plot these points on a graph and draw the line that passes through them.

The graph of the equation x - 3y = -7 is a line passing through the points (1, 4/3), (2,5/3), (3,6/3) and the y-intercept is (0,7/3)

The equivalent expression for [tex](125x^{\frac{7}{3}})^{\frac{-1}{3}}[/tex] is [tex]\frac{1}{5x^{\frac{7}{9} }}[/tex].

The exponent of a number tells that how many times its original value has been multiplied by itself. Exponent-related issues are solved using the rules of exponents or the characteristics of exponents. These characteristics are regarded as important exponents principles that must be adhered to while solving exponents. The characteristics of exponents are extensively used in mathematics, particularly in algebra. We can simply simplify the formulas and write them in fewer steps with the use of the exponent's characteristics.

Law of Power of a Power: (xᵃ)ᵇ = xᵃᵇ

The given expression is [tex](125x^{\frac{7}{3}})^{\frac{-1}{3}}[/tex]

Use the property of exponents to get

= [tex](125^{\frac{-1}{3} } \times x^{\frac{7}{3}\times{\frac{-1}{3}}})[/tex]

As, [tex]125^{\frac{1}{3} }[/tex] = 5

= [tex](5x)^{\frac{-7}{9} }[/tex]

= [tex]\frac{1}{5x^{\frac{7}{9} }}[/tex]

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The table is not linear nor exponential.

Hence, The answer is neither.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

We know that;

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the table, we can make coordinates points.

(-10, 3)

(-5, 30)

(0, 300)

(5, 3000)

If the relationship is linear we must have the rate of change between two coordinates equal.

Rate of change between (-10, 3) and (-5, 30) is,

⇒ (30 - 3) / (- 5 - (-10))

⇒ 27 / 5

And, Rate of change between (-5, 30) and (0, 300)

⇒ (300 - 30) / (0 - (-5))

⇒ 270 /  5

⇒ 270/5

So, The relation is not a linear relation.

Now, If we plot the graph we get a curve shape.

This means, The relation is not exponential.

Thus, The table is not linear nor exponential.

The answer is neither.

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Given g is a one-to-one function

g(1) = 5

g-1(5) = 1

Given h is a one-to-one function

h(x) = 4x + 9

y = 4x + 9

(y-9)/4 = x

h-1(x) = (x-9)/4

(h-1°h)(-2) = h-1(h(-2))

= h-1(1) [ as h(-2) = 1]

= (1-9)/4

= -2

The number of different delegations of six that can be formed if at least four are seniors is; 31119

Permutations and combinations, are simply the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

In this question we will be making use of the combination formula which is; [tex]^{n} C_{r}[/tex] = n!/(r!(n - r)!)

The parameters are;

Number of senior leaders = 12

Number of Junior Leaders = 10

Thus, the solution is;

(¹²C₄ * ¹⁰C₂) + (¹²C₅ * ¹⁰C₁) + (¹²C₆ * ¹⁰C₀)

= (495 * 45) + (792 * 10) + (924 * 1)

= 22275 + 7920 + 924

= 31119

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On solving the provided question we cans ay that the exact value of trigonometry cos x = 5/13

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

the exact value of cot x = 5/12  

cos x = we have to find

cot x = b/p

cos x = 5/13

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The x-values are the inputs.

The y-values are the outputs.

The missing value in the table for x = –1 is y = 6.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

Conversely, a range is the set of all possible output numerical values (y-values) to a function and the range of a graph comprises all the output numerical values (real numbers) which are located on the y-coordinate.

Note: The coefficient of this equation y = 2 – 4x is 4.

When x = -1, the range (y-value) can be calculated as follows;

y = 2 – 4x

y = 2 – 4(-1)

y = 2 + 4

y = 6.

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Answer:

1.5

Step-by-step explanation:

of means multiplied by.

Therefore, 1/4×6

=6/4

=1.5

A description which best compares the graph given by the equations 2x - 7y = -5 and x - 3y = 4 include the following: D. intersecting but not perpendicular.

In Mathematics, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below by both line m and line n.

Generally speaking, it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).

By critically observing the graph of the lines representing equations 2x - 7y = -5 and x - 3y = 4, we can reasonably infer and logically deduce that they both intersect, but are not perpendicular because the angle of intersection is not an angle of 90° (right angles).

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Complete Question:

Which description best compares the graph given by the following equations:

2x - 7y = -5

x - 3y = 4

parallel

coinciding

perpendicular

intersecting but not perpendicular

The relation between number of roses and number of rose plants are non proportional.

We know that,

A proportional variation exists when a relationship between two variables, x and y, can be expressed in the form y/x = k

where

k is a constant

Here,

Let,

A = (2,35)

B = (4,30)

Find the slope m,

m = y2 - y1 / x2 - x1

Substitute the values in the formula,

m = 30 - 35 / 4 - 2

m = -5/2

Find the equation of the line with m and the point A,

y - y1 = m(x - x1)

y - 35 = -5/2(x - 2)

y - 35 = -5/2x - 5

y = -5/2x + 30

x is the number of rose plants.

y is the the number of roses.

So,

The relationship between the number of rose plants and the number of roses is not in ratio.

Therefore the relationship is non-proportional.

The complete question:

"the relationship between the number of rose plants and the number of roses is Proportional Or Non Proportional."

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The slowest way of getting to 1000 from 1 by increments of 3 would be to increment the number by 1 each time, reaching 1000 in 1000 steps.

The slowest way to reach 1000 from 1 by increments of 3 would be to add 3 to the number one step at a time until you reach 1000.

This would take the maximum amount of steps because the increments are small compared to the goal number. For example:

1 + 3 = 4

4 + 3 = 7

7 + 3 = 10

...

997 + 3 = 1000

In this case, it would take 334 steps to reach 1000, which is the slowest way to reach 1000 using increments of 3.

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The class limits for a frequency table with seven classes having lowest and highest limit as 20 and 94 respectively is -

1: 20 - 31

2: 32 - 43

3: 44 - 55

6: 56 - 67

7: 68 - 79

What is a frequency table?

The frequency of a specific data value refers to how frequently it appears in a particular data set. The lists of items in a given data collection and the number of times each item appears in the data set make up a frequency table.

The minimum value for the data set is, = 20

The maximum value for the data set is, = 94

The number of classes in the frequency table is, = 7

To find the width of the class use the formula -

Width = Range / Number of classes

Range = Maximum value - Minimum value

Plugging in all the values in the equation -

Width = (94 - 20) / 7

Width = 74/7

Width = 10.71 ≈ 11

Now, the class limits will start from the lower limit = 20.

Each class will have a range of 11.

The class limits are -

1: 20 - 31

2: 32 - 43

3: 44 - 55

6: 56 - 67

7: 68 - 79

8: 80 - 82

9: 83 - 94

Therefore, the class limits for obtained.

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Answer:

18°

Step-by-step explanation:

m<HLG+ m<HLI =90° being right angle

(9m)°+(25m+22)°=90°

9m°+ 25m°+22°=90°

34m°=90°-22°

34m°=68°

m°=68°/34°=2

since m<HLG =9m°=9*2°=18°

Answer:

3/4

Step-by-step explanation:

First, make the denominator of 1/2 equal to the denominator of 11/12. We know 2x6=12. So we must multiply the numerator of 1/2 (1) by 6. We would get the answer 6/12. We must now subtract the numerators. 11-6=5. That leaves us with 5/12+2/6. Now we must do the same to 2/6. 2x6=12. Then, 2x2=4. That leaves us with 5/12+4/12=9/12. Now to simplify, we must find a common divider. We know 9 can be divided by 3, and so can 12. 9/3=3. 12/3=4. Final answer is 3/4.

Answer:

A / M

B / K

C / I

D / J

E / P

F / O

G / L

H / N

Step-by-step explanation:

Hope this helped! : D

The value of x is 16.8

If two triangles' I) corresponding angles and (ii) corresponding sides are equal, two triangles are said to be similar. (The ratio of adjacent sides' lengths is equal.)

•Triangle similarity should be expressed symbolically using the correct vertices' correspondence.

Take 2 pictures as ∆ABC and ∆PQR

∆ABC ~  ∆PQR

AB = 15 cm  , BC = 12 cm , PQ = 21 cm , QR= x cm

AB /PQ = BC/QR

15 /21 = 12/x

5/7 = 12/x

84/5 = x

x   =   16.8

so   the value of x is 16.8

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Using the t-distribution, the 96% confidence interval for the average number of hours of sleep for  students is between 6.057 and 6.943 hours.

The calculation for the confidence interval is:

the sample mean

t is the critical value

s  the sample standard deviation

n is the sample size

Ptting  the given values, we have:

6.5 ± 2.081  x (2.14/sqrt(101))  

Which simplifies to

6.5 ±  2.081 x  (0.2129)

So, the 96% confidence interval for the average number of hours of sleep for working college students is between

6.5 - (0.4431) = 6.057

6.5 + (0.4431) = 6.943

The 96% confidence interval for the average number of hours of sleep for working college students is between6.057 and 6.943 hours.

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Answer: 2/3, 5/6, 3/4

Step-by-step explanation:

Answer:

[tex] \frac{2}{3} \: \frac{3}{4} \: \frac{5}{6} [/tex]

Step-by-step explanation:

[tex] \: \: \: \frac{2}{3 } \: \: \frac{3}{4} \: \: \: \frac{5}{6} \\ = \frac{8}{12} \frac{9}{12} \frac{10}{12} [/tex]