Which of the following systems of inequalities has Point C as a solution?

A:
[tex]f(x)\leq 3x+4\\g(x)\leq -\frac{1}{2} x-5\\[/tex]

B:
[tex]f(x)\geq 3x+4\\g(x)\leq -\frac{1}{2} x-5[/tex]

C:
f(x) ≤ 3x + 4
[tex]g(x)\geq -\frac{1}{2}x-5[/tex]

D:
f(x) ≥ 3x + 4
[tex]g(x)\geq -\frac{1}{2} x-5[/tex]

To find the width of each strip, divide the total width of the cloth by the number of strips required.

To find the width of each strip, we need to divide the total width of the cloth by the number of strips required. Let's assume the width of the cloth is W. So, each strip would get a width of W/10.

Answer:

The distance cover by Mai's bike is 2 time the distance cover by Noah's bike

Step-by-step explanation:

Given as :

The distance cover by Mai's bike = [tex]d_1[/tex] = 7 [tex]\dfrac{1}{4}[/tex] miles

I.e [tex]d_1[/tex] = [tex]\dfrac{28+1}{4}[/tex] miles

Or, [tex]d_1[/tex] = [tex]\dfrac{29}{4}[/tex] miles

The distance cover by Noah's bike = [tex]d_2[/tex] = 3 [tex]\dfrac{5}{8}[/tex] miles

I.e [tex]d_2[/tex] = [tex]\dfrac{24 + 5}{8}[/tex] miles

Or,  [tex]d_2[/tex] = [tex]\dfrac{29}{8}[/tex] miles

let the number of times that Noah's bike ride was Mai's bike ride = n

So, The distance cover by Mai's bike = n × The distance cover by Noah's bike

Or, [tex]d_[/tex] = n ×  [tex]d_[/tex]

Or, [tex]\dfrac{29}{4}[/tex] miles =  n × [tex]\dfrac{29}{8}[/tex] miles

Or, n = [tex]\frac{\frac{29}{4}}{\frac{29}{8}}[/tex]

∴ n = [tex]\dfrac{8}{4}[/tex]

I.e n = 2

Hence The distance cover by Mai's bike is 2 time the distance cover by Noah's bike  . Answer

A.

(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)

Answer:

A.

(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)

Thats the correct answer.

Answer:

n+16

Step-by-step explanation:

21+(n-5)=21+n-5=n+21-5=n+16

The sum of slopes b and c is 0

This statement is NOT always true

Step-by-step explanation:

(1) According to the graph, line a and b are parallel to each other. This, therefore, means that they have the same slope/gradient.

(2) Line c however, is perpendicular to both lines a and b. The slope of two lines that are perpendicular to each other is always the negative inverse of the slope of the other. This means that the product of their slopes will become -1.

An example is that if the slope of a line is 2, then a line perpendicular to it will have a slop of – ½

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Answer:

The sum of the slopes of line b and line c is 0

Step-by-step explanation:

Verify each statement

case a) The sum of the slopes of line b and line c is 0

we know that

Line b and line c are perpendicular lines

If two lines are perpendicular, then their slopes are opposite reciprocal

If the slope of line c is n

then the slope of line b is -1/n

[tex]-\frac{1}{n}+n=0[/tex]

Solve for n

[tex]n^{2}=1[/tex]

[tex]n=\pm1[/tex]

That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1

therefore

NOT always true

case b) Line a and line b have the same slope

This statement is always true, because the lines are parallel

Remember that

If two lines are parallel, then the lines have the same slope

case c) The product of the slopes of line a and line c is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

case d) The product of the slopes of line c and line b is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex] and [tex]81/7.[/tex] The second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric.

Let's denote the three numbers forming the geometric progression as [tex]a[/tex], [tex]ar[/tex], and [tex]ar^2}[/tex], where a is the first term and [tex]r[/tex] is the common ratio.

If the second term is increased by [tex]2[/tex], then the progression becomes arithmetic. This means:

[tex]ar+2=2ar-a[/tex]

[tex]2=ar-a \\2=a(r-1)[/tex]

If after this, the last term is increased by [tex]9[/tex], then the progression becomes geometric again. This means: [tex]ar^2} +9=(ar+2)r[/tex]

[tex]ar^2} +9=ar^2} +2r \\9=2r \\r=9/2[/tex]

Now, we have found the value of [tex]r[/tex], which is the common ratio. Let's substitute [tex]r=29[/tex] into the equation [tex]2=a(r-1)[/tex] to find the value of a:

[tex]2=a((9/2)-1) \\2=a(9-2/2) \\2=a(7/2) \\a=4/7[/tex]

So, the first term a is [tex]4/7.[/tex]

Now, let's find the second term by substituting [tex]a=4/7[/tex] into the equation [tex]ar+2=2ar-a:\\4/7.9/2+2=2.4/7.9/2-4/7 \\18/7+2=36/7-4/7 \\32/7=32/7[/tex]

This equation is satisfied, so the second term is [tex]32/7.[/tex]

Finally, let's find the third term by multiplying the first term by the common ratio:

[tex]4/7.(9/2)2=7.4/4.1/8=81/7[/tex]

So, the three numbers forming the geometric progression are [tex]4/7, 32/7,[/tex]and [tex]81/7.[/tex]

We used the properties of geometric and arithmetic progressions to set up and solve equations to find the three numbers. First, we found the common ratio r by solving the equations derived from the given conditions. Then, we found the first term a and used it to find the second term. Finally, we found the third term by multiplying the first term by the common ratio squared.

COMPLETE QUESTION:

Three numbers form a geometric progression. If the second term is increased by [tex]2[/tex], then the progression will become arithmetic and if, after this, the last term is increased by [tex]9[/tex], then the progression will again become geometric. Find these three numbers.

The three numbers are 4, 18, and 81.

Let the three numbers forming the geometric progression be [tex]\( a, ar, \)[/tex] and [tex]\( ar^2 \)[/tex], where [tex]\( r \)[/tex] is the common ratio.

Given that increasing the second term by 2 makes it an arithmetic progression, we have:

[tex]\[ar + 2 = a + 2d\][/tex]

where d  is the common difference in the arithmetic progression.

Similarly, after increasing the last term by 9, the progression becomes geometric again, so:

[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]

From the first equation, [tex]\( d = (ar - a)/2 \)[/tex], and substituting this into the second equation, we get:

[tex]\[ar^2 + 9 = (ar + 2)r\][/tex]

[tex]\[ar^2 + 9 = ar^2 + 2r\][/tex]

[tex]\[9 = 2r\][/tex]

[tex]\[r = \frac{9}{2}\][/tex]

Substituting [tex]\( r = \frac{9}{2} \)[/tex] into the first equation, we find [tex]\( d = \frac{a}{2} \)[/tex].

Thus, [tex]\( a + 2 = a + \frac{a}{2} \)[/tex], and solving for [tex]\( a \)[/tex], we find [tex]\( a = 4 \)[/tex].

Then, using [tex]\( r = \frac{9}{2} \)[/tex], we find [tex]\( ar = 18 \) and \( ar^2 = 81 \)[/tex].

Therefore, the three numbers are 4, 18, and 81.

Answer: The variable is 3.

Step-by-step explanation: 5x3=15. 15+8=23

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Answer:

Below in bold.

Step-by-step explanation:

sin ^2x + cos ^2 x = 1, so

cos^2x = 1 - (5/11)^2 = 96/121

cos x = √96/11

= 4√6/11.

sin 2x = 2 sinx cosx  = 2 * 5/11 * 4√6/11.

= 40√6/121.

cos2x =  2cos^2 x - 1

= 2 * 96/121 - 1

=  192/121 - 121/121

= 71/121.

Final answer:

To form the quadratic equation, we consider the original time to cover 6 km at speed v km/h and the new time at speed (v+2) km/h, then equate the difference in time to 4 minutes. Solving for v using a common denominator and simplifying, we obtain the quadratic equation 15v^2 + 30v - 90 = 0.

Explanation:

To form a quadratic equation from the given scenario, we’ll first define the relationship between distance, speed, and time. The time taken to travel 6 km at the original speed v km/h is distance divided by speed, which is 6/v hours. If Wanni increased her speed by 2 km/h, her new speed would be v + 2 km/h, and the new time taken would be 6/(v+2) hours.

We are told that by increasing her speed, Wanni arrives 4 minutes earlier. Since 1 hour is 60 minutes, 4 minutes is 4/60 or 1/15 hours. We can now set up an equation relating the difference between the two times to 1/15 hours:

6/v - 6/(v+2) = 1/15

To solve for v, we first find a common denominator for the fractions on the left side of the equation, which is v(v+2). Multiplying both sides by the common denominator, we get:
6(v+2) - 6v = v(v+2)/15

Expanding the terms and moving everything to one side of the equation, we get our quadratic equation in terms of v:

15v2 + 30v - 90 = 0

Answer:

The probability of winning = 0.001 and hence the expected payoff = $0.

Step-by-step explanation:

There is a lottery contest and there are 1000 entries.

Only one will win and will get a prize of $710. All others would be given nothing.

We have to find the probability of the person winning.

Probability = [tex]\frac{number of favorable events}{total number of events}[/tex]

Number of favorable events = 1

Total number = 1000

So probability of winning the payoff = [tex]\frac{1}{1000}[/tex] = 0.001

Hence the expected payoff = $0

Answer:

The volume of the larger solid is [tex]592.6\ mm^3[/tex]

Step-by-step explanation:

The question is

If these solids are similar, find the volume of the larger solid

step 1      

Find the scale factor

we know that

If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

x ----> the height of the larger solid in mm

y ----> the height of the smaller solid in mm

z ---> the scale factor

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=4\ mm\\y=3\ mm[/tex]

substitute

[tex]z=\frac{4}{3}[/tex] ---> scale factor

step 2

Find the volume of the larger solid

we know that

If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

x ----> the volume of the larger solid in cubic millimeters

y ----> the volume of the smaller solid in in cubic millimeters

z ---> the scale factor

[tex]z^3=\frac{x}{y}[/tex]

we have

[tex]z=\frac{4}{3}[/tex]

[tex]y=250\ mm^3[/tex]

substitute the values

[tex](\frac{4}{3})^3=\frac{x}{250}[/tex]

solve for x

[tex](\frac{64}{27})=\frac{x}{250}[/tex]

[tex]x=250(\frac{64}{27})[/tex]

[tex]x=592.6\ mm^3[/tex]

Answer:

Step-by-step explanation:

The complete question is

A scale factor of 1/3 is used to make a reduction, as shown in table below.

What is the base of the reduced triangle?

According to the given table, the original base is 24. If the given scale factor is applied, the reduced base would be

[tex]\frac{1}{3}24=8[/tex]

Remember that a scale factor is a number that multiples the figure, a scale factor can reduced or amplify a figure.

Therefore, the reduced base is 8 units.

Answer:

8 units

Step-by-step explanation:

Answer:

max.600,000

min.595,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

f(x) = x³ - x² - 6x

Step-by-step explanation:

If a polynomial f(x) has roots x = a and x = b then the factors are

(x - a) and (x - b) and the polynomial is the product of the factors, that is

f(x) = (x - a)(x - b)

Here the roots are x = 3, x = - 2 and x = 0, thus

(x - 3), (x - (- 2)) and (x - 0) are the factors, that is

(x - 3), (x + 2) and x , hence the polynomial is

f(x) = x(x - 3)(x + 2) ← expand the pair of factors

     = x(x² - x - 6) ← distribute parenthesis by x

     = x³ - x² - 6x

Answer: 1

Step-by-step explanation:

6 times 2 minus 2y = 10

first 6x2=12

12-2y=10

minus 12 from each side =0

so now you have;

-2y= -2

divide & you get one!

<33333

Answer:

D Y=4x-15

Step-by-step explanation:y=Mx+b

Answer:

[tex]k=\frac{32}{5}[/tex],  [tex]y=\frac{32}{5}x[/tex]

[tex]k=6.4[/tex], [tex]y=6.4x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Find the value of the constant of proportionality k

take any ordered pair from the data

For x=25, y=160

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{160}{25}[/tex]

simplify

[tex]k=\frac{32}{5}[/tex]

The linear equation is equal to

[tex]y=\frac{32}{5}x[/tex]

or

[tex]y=6.4x[/tex]

The school council will have 216 small sandwiches.

Step-by-step explanation:

Sandwiches ordered = 12

Length of one sandwich = 6 feet

1 foot = 12 inch

6 feet = 12*6 = 72 inches

Length of one sandwich in inches = 72 inches

As one small sandwich is 4 inches,

Number of small sandwiches in one sandwich = [tex]\frac{72}{4}=18[/tex]

One sandwich = 18 small sandwiches

12 sandwiches = 18*12 = 216 small sandwiches

The school council will have 216 small sandwiches.

Keywords: multiplication, division

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Answer:

16

Step-by-step explanation:

8(19-17)=8(2)=16

Answer

           -1

Step-by-step explanation:

Answer:

The new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Step-by-step explanation:

The rule for rotation a point 180° counterclockwise about the origin states that when a point (x, y) is rotated 180° counterclockwise about the origin, the new position of the coordinates of point P(x, y) becomes (-x, -y).

Hence,

So, when the given point  (-4,0) is rotated 180 degrees counterclockwise using center (0,0), the new coordinates of the image will be:

Therefore, the new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Keywords: rotation, origin, image

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The mean of 3.7,5, 9.2,4,6.1,5,2.6, 4,5.2,5 is 4.88.

Mean is referred in mathematics to as average of the mentioned numbers. Average can be virtually imagined as a center position giving every number equal weight. Average can be calculated by diving the sum of all the numbers by count of total numbers.

For example, 2, and 4 will have average of 3. Average of 2,3,4 will be also 3. This is because [tex]\frac{(2+4)}{2} = 3, and\ also\ \frac{(2+3+4)}{3} = 3[/tex].

So considering the above Question, count of all the above numbers is 10.

Sum = 3.7 + 5 + 9.2 + 4 + 6.1 + 5 + 2.6 + 4 + 5.2 + 5 = 488

Mean = Average = [tex]\frac{Sum}{Count}[/tex]

Mean = [tex]\frac{488}{10}[/tex] = 4.88

Answer:

its 4.88

Step-by-step explanation:

it was on my test

Answer:

[tex]w=8.06[/tex]

Step-by-step explanation:

Given statement:

[tex]w[/tex] divided by -1.3 equals -6.2

The above statement can be written mathematically as:

[tex]\frac{w}{-1.3}=-6.2[/tex]

We need to solve for [tex]w[/tex].

Multiplying both sides by -1.3 to remove fraction and isolate [tex]w[/tex] on one side.

[tex]-1.3\times \frac{w}{-1.3}=(-6.2)\times (-1.3)[/tex]

∴ [tex]w=8.06[/tex]    [Product of two negatives is a positive]

Answer:

w = 8.06

Step-by-step explanation:

Answer: I believe it’s -4/5

Step-by-step explanation:

Answer:

Yes, because when waves are at the same place at the same time, the amplitudes of the waves simply add together and this is really all we need to know!

Step-by-step explanation:

The sum of two waves can be less than either wave, alone, and can even be zero. This is called destructive interference.

If we place the waves side-by-side, point them in the same direction and play the same frequency, we will have  constructive interference.

Answer:

16.5.

Step-by-step explanation:

This is an arithmetic series because the increase is a constant 0.30.

Sum of n terms = (n/2)[a + l)    where n = no.of terms a = first term , l = last term.

There are 3/ 0.3 = 10 terms so

Sum = (10/2) (0.3 + 3.0)

= 5 * 3.3

= 16.5.

Answer:

Infinitely many solutions

Step-by-step explanation:

the 5x's cancel and -15 + 6 = -9 so -9 equals -9. No matter what value you input for x, the answer is equal.

Answer:

Infinitely  many.

Step-by-step explanation:

5(x - 3) +6= 5x - 9

5x - 15 + 6 = 5x - 9

5x - 9 = 5x - 9.

We can enter any real value of x and both sides will be equal so there are infinitely many solutions.

Answer:

25. rational

26. irrational

Step-by-step explanation:

A rational number is a number that can be written as a fraction. It may have decimals that end or repeating decimals.

An irrational number cannot be written as a fraction. It's decimals continue on and do not repeat.

25.

When you multiply two rational numbers, the product is rational. The square root of 16 is 4, which is rational because it is a whole number. 4/7 is written as a fraction so it is rational.

26.

The square root of 2 is an irrational number because its decimals go on and do not repeat. 7 is a whole number so it is rational. Subtracting a irrational number from a rational number gives an irrational number.

Answer:

2514

Step-by-step explanation:

Do the long division and you'll find the answer.

Answer:

4/3 is 1.3333333333,so the range of it is that