Determine whether the statement is always, sometimes, or never true. Explain you reasoning.
Lines p and q intersect in points M and N .

For the given set of inequality, the value of x is 8.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Given, the equation is -

x+ 3 > 19 = 3x

⇒ x + 3 > 19 - 3x

Subtracting 3 from bot sides

⇒ x > 16 - 3x

subtracting x from both sides

⇒ 16 - 2x > 0

⇒ x = 8

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27.9 cm≤ perimeter ≤28.5cm

The length of the regular hexagon is 4.7cm to 1 decimal place, i.e.,

4.65≤ length≤4.75

As we know the number of sides of a regular hexagon is 6

So the perimeter for the upper bound of length = 6×4.65

                                                                                = 27.9cm

The lower bound of length perimeter = 6× 4.75

                                                              = 28.5cm

Therefore the interval of the perimeter of a regular hexagon is:

27.9cm ≤ perimeter ≤ 28.5cm

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The total number of signals that can be made using 5 flags from 8 flags of different colors is 6720.

Permutations:

A permutation is an act of arranging the objects or numbers in order.

The formula for permutations is:

nPr = n!/(n-r)!

where

nPr = permutation

n = total number of objects

r = number of objects selected

Combinations:

Combinations are the way of selecting the objects or numbers from a group of objects or collection, and the order of the objects does not matter.

The formula for combinations is:

nCr = n!/[r! (n-r)!]

Where,

nCr  = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Given,

Here we need to find how many different signals can be made with 5 flags from 8 flags of different colors.

The number of ways that 5 flags can be selected is the combination of 8 flags taken 5 at a time.

After choosing 5 flags from 8, it can be arranged in

=> ₅P₅ ways = (5!)

Therefore, the total number of signals that can be made is

=> ₈C₅ x  ₅P₅

=> (8!/(8-5)!5!) x 5!

=> (8! / 3!)

=> 40320 / 6

=> 6270

Therefore, the total number of signals that can be made is 6270.

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The correct answer is option (a) 70° is the possible measures of A.

Given that, the isoceles triangle's base angles are equal

let angle D be its vertical angle.

With angle E equal to angle F

angle D+ angle E+ angle F=180'

angle D+ 55'+55'=180',

angle D+ 110'=180'

angle D=180'-110'

angle D=70'.

Figure DEF is an isosceles triangle. The measure of A is 55°, while the measure of B is 70°. As there are two possible measures of D, it can be calculated that the base area equal to 426 square units and the height equals 232 square units.

Hence, 70° is the possible measures of A.

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Answer:

[tex]y=-\frac{5}{6} (x-6)+1[/tex]

Step-by-step explanation:

Using point slope form:

[tex]y=m (x-x_1)+y_1[/tex]

Put in the given parameters:

[tex]m=-\frac{5}{6}[/tex]

[tex]x_1=6[/tex]

[tex]y_1=1[/tex]

Now get the solution:

[tex]y=-\frac{5}{6} (x-6)+1\\[/tex]

For I = [tex]\sqrt{W/R}[/tex]  gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.

As given in the question,

Formula  I = [tex]\sqrt{W/R}[/tex]

I = electric current in amperes

W = power in watts

R = Resistance in ohms

When W = 500 , R = 100

I = [tex]\sqrt{500/100}[/tex]

⇒ I = [tex]\sqrt{5}[/tex] amperes

Therefore, for I = [tex]\sqrt{W/R}[/tex]  gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.

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Answer:

no it is not because natural numbers are whole numbers :)

hope this was helpful!

Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

PS you cant leave out exponents when typing questions without the attached photo. multiplying by 2 is not the dame as a exponent of 2. Use ^2 to show that a number is to the power of 2.

the value of p(2) in this equation is 2.

Answer:

p(2) = 2

Step-by-step explanation:

substitute x = 2 into p(x)

p(2) = - 3(2 - 4)² + 14

      = - 3(- 2)² + 14

      = - 3(4) + 14

      = - 12 + 14

      = 2

Answer:

6,666

Step-by-step explanation:

A four-digit number: 1,234

All digits are the same: 1111, 2222, 3333...

Value in the hundreds place: 0,600

Answer: 6,666

The equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

The given parameters are:

The above means that

Total = Cheese + Bags of lemon * 5

This gives

24.36 = 5.31 + 5 * x

Collect the like terms

So, we have

24.36  - 5.31 = 5 * x

Evaluate the like terms

So, we have

19.05 = 5 * x

Divide through by 5

So, we have

x = 3.81

Hence, the equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

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Answer: If (4, y ) is an ordered pair of the function, then y = 1

Step-by-step explanation:

The known x coordinate for the position (4,y) is 4.

We'll just refer to it as y since we don't know the y coordinate just yet.

On the x axis, trace a vertical line through 4 (see related remark below).

Thus in red (see attached image).

The red line crosses the graph at the point (4,1)

so this tells us that,

                                          y = 1

Although it's helpful to see how it turns out, you are not need to draw a vertical red line.

You will be able to visually perceive the solution without these extra lines after you become accustomed to these kinds of situations.

Therefore,

If (4, y ) is an ordered pair of the function, then y = 1

                               y = 1

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Answer: Options 3, 4, 6

Step-by-step explanation:

[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]

This means are looking for lines with a slope of 4 (since parallel lines have the same slope).

Answer:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6

Step-by-step explanation:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6

The total distance traveled by the pendulum when it comes to rest is 10,000 cm.

Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .

Now,

Given,

On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.

The first term of the geometric sequence is, a1 = 100

The second term of the sequence is, a2 = 99

The common ratio r = 99/100

Therefore, the expression for the n-t h term of the sequence is:

a_n = 100*(99/100)^(n-1)

Theoretically, using this formula, it would take an infinite number of trips to come to rest.

Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.

The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.

Therefore,

the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm

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A logarithm is a power that requires a number to be raised to another power. The bases of all the values involved must be identical. So, we must create equivalent expressions in the equation that all have equal bases. And the two expressions then formed can only be said equal if the exponents are also similar. Now we will move towards the solution to the problem.

Solution:

log (5,25)

log (5,25)

=log (25) log (5)

=log (52) log (5)

=2log (5) log (5)

=2

2nd Solution:

log (5,25) =2

Solution steps:

=log (5,25)

=log5(25)

=2

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Answer: y=24

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

A+B=180

3y + 12 + 2y +48=180

3y+2y+12+48=180

5y+60=180

5y=120

y=24

The commutative property [tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex] has been proved.

Commutative property:

The commutative property states that the changes the order or position of two numbers while adding or multiplying them does not change the end result.

The general form of commutative property is

A + B = B + A

For example, while adding the number 4, and 5

4 + 5 = 5 + 4 = 9.

Which means both yields the same result.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Now we need to prove the commutative property[tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex].

We know that,

"The vectors are defined as an object containing both magnitude and direction. Vector describes the movement of an object from one point to another."

Based on the commutative property,

We have to to apply the value of [tex]\overrightarrow{a}[/tex]and[tex]\overrightarrow{b}[/tex] to the equation,

Then we get,

[tex]\implies\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex]

=> <x₁, y₁> + <x₂, y₂> = <x₂, y₂> + <x₁, y₁>

While looking at the expression we know that,

Both are equal.

Then the commutative property has been proved.

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Answer: 7.5

Step-by-step explanation: 15 ft * 2 in/ft = 30 in18 ft * 2 in/ft = 36 inso area on plan = 30*36 = 1080 in^2on the real size area = 15*18 = 270 ft^2well to compare them change in^2 to ft^2there are 12 in /ftso 144 in^2 per ft^2so1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2or you could say30 in = 30/12 ft36 in = 3 ftarea = 90/12 ft^2 = 7.5 ft^2 luckily :)

The slope of the given points are  (29, 11) and (-3, -7):

= 0.5625.

A line's slope indicates whether sharp it is.. The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

In general, a line's slope indicates its steepness as well as direction. The slope of a straight line connecting two points (x1,y1) and (x2,y2) can be simply calculated by subtracting the coordinates of both the points. The slope is commonly denoted by the letter'm.'

X₁ = 29

Y₁ = 11
X₂ =  -3
Y₂ = -7

The slope is the degree of tilt a line has and it may be positive, negative, zero, or undefined.

slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the value in the given formula:

slope  =  [tex]\frac{(-7 - 11)}{(-3 - 29)}[/tex]

          = -18 / -32

          = -9 / -16

          = 0.5625

The slope of the given points are  (29, 11) and (-3, -7) = 0.5625.

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Answer:

Alternate Exterior ANgles

Step-by-step explanation:

A symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.

Symmetry:

Rotational symmetry:

Relation:

Therefore, a symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.

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30 - The amount he earns every week

12 - the fee for one hour of lawn service without the base fee

12h - the cost for h hours of lawn service without the base fee

Hope this helps you!! :3

Answer:

13/6

Step-by-step explanation:

1 Simplify  \sqrt{8}

8

​

  to  2\sqrt{2}2

2

​

.

\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

6×2

2

​

2

​

2

​

−(−

81

​

18

​

)

2 Simplify  6\times 2\sqrt{2}6×2

2

​

  to  12\sqrt{2}12

2

​

.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

12

2

​

2

​

2

​

−(−

81

​

18

​

)

3 Since 9\times 9=819×9=81, the square root of 8181 is 99.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})

12

2

​

2

​

2

​

−(−

9

18

​

)

4 Simplify  \frac{18}{9}

9

18

​

  to  22.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)

12

2

​

2

​

2

​

−(−2)

5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}

12

2

​

2

​

⋅

2

​

2

​

​

=

12×2

2

2

​

​

.

\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)

12×2

2

2

​

​

2

​

−(−2)

6 Simplify  12\times 212×2  to  2424.

\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)

24

2

2

​

​

2

​

−(−2)

7 Simplify  \frac{2\sqrt{2}}{24}

24

2

2

​

​

  to  \frac{\sqrt{2}}{12}

12

2

​

​

.

\frac{\sqrt{2}}{12}\sqrt{2}-(-2)

12

2

​

​

2

​

−(−2)

8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}

b

a

​

×c=

b

ac

​

.

\frac{\sqrt{2}\sqrt{2}}{12}-(-2)

12

2

​

2

​

​

−(−2)

9 Simplify  \sqrt{2}\sqrt{2}

2

​

2

​

  to  \sqrt{4}

4

​

.

\frac{\sqrt{4}}{12}-(-2)

12

4

​

​

−(−2)

10 Since 2\times 2=42×2=4, the square root of 44 is 22.

\frac{2}{12}-(-2)

12

2

​

−(−2)

11 Simplify  \frac{2}{12}

12

2

​

  to  \frac{1}{6}

6

1

​

.

\frac{1}{6}-(-2)

6

1

​

−(−2)

12 Remove parentheses.

\frac{1}{6}+2

6

1

​

+2

13 Simplify.

\frac{13}{6}

6

13

​

Done

Inequality is [tex]p + 31 \ge 85[/tex]

Solution is [tex]p \ge 54[/tex]

===============================================

Explanation:

p = number of pages left to read

31 = number of pages already read

p+31 = total number of pages (unread + read)

This total must be 85 or larger, so that's how we end up with [tex]p+31 \ge 85[/tex]

To solve this inequality, we subtract 31 from both sides to end up with [tex]p \ge 54[/tex] which means Jen still needs to read at least 54 pages.

The mean of the salary is $120000.

By adding up a list of salaries and dividing by the total number of salaries on the list, mean salaries are derived. This means that exceptionally high and extremely low incomes have the same weight in the final average, which is crucial to bear in mind while investigating industry salaries.

By ranking the wages of a group of employees in descending order, you may determine the median base salary by finding the income that is in the middle of the distribution.

Mean=(5*440,00+2*100,000+1*540,000)/(5+2+1)

         =(220,000+200,000+540,000)/8

         =960,000/8

         =120,000

Median is 100,000.

Hence, the mean salary is 120,000 but 7/8  members salary is lower than 120,000. Because the firm’s owner salary is too high. thus the firm’s owner is so unethical regarding employee salary.

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The angle of elevation of the ramp to the nearest degree is 8°

From the information given, we have the following deductions;

The tangent identity is expressed as;

tan θ = opposite/ adjacent

substitute the values

tan θ = 2/ 15

find the ratio

tan θ = 0. 1333

Find the tangent inverse of the value

θ = [tex]tan^-^1(0. 1333)[/tex]

θ = 7. 79 °

θ = 8° in the nearest degree

Thus, the angle of elevation of the ramp to the nearest degree is 8°

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Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°

An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.

This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.

All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.

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Answer: give me the context please

Step-by-step explanation: