A 4.5-m rope is attached to a 5.4-m rope. However, when the ropes are tied, 4 cm of length is lost to form the knot. What is the length of the tied ropes?

Given a quadratic equation of the form:

The discriminant is:

And we can know the number of solutions with the value of the discriminant:

• If D < 0, the equation has 2 imaginary solutions.

• If D = 0, the equation has 1 real solution

• If D > 0, the equation has 2 real solutions.

Equation One:

Then, we calculate the discriminant:

D = 0

There are 1 real solution.

Equation Two:

Calculate the discriminant:

D = -116

There are 2 imaginary solutions.

Equation Three:

Calculate the discriminant:

D = 100

There are 2 real solutions.

Answers:

Equation 1: D = 0, One real solution.

Equation 2: D = -116, Two imaginary solutions.

Equation 3: D = 100, Two real solutions.

Answer:

Step-by-step explanation:

If we assume the length and width are integer numbers of centimeters, we can look at the factors of 330:

  330 = 1×330 = 2×165 = 3×110 = 5×66 = 6×55 = 10×33 = 11×30 = 15×22

The factors in this last pair differ by 7, so represent the width and length of the rectangle.

The rectangle's length and width are 22 cm and 15 cm, respectively.

The term, \(\frac{1}{49}\) is simplified form of the expression \(7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}\).

The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.

Additionally, lowest terms, or simple form, may be used.

The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.

Given to simplify the expression

\(7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}\)

\(7^{(-\dfrac{5}{6}-\dfrac{7}{6})}\)

\(7^{(\dfrac{-5-7}{6})}\)

\(7^{(\dfrac{-12}{6})}\)

\(7^{(-2)}\)

\(\dfrac{1}{7} \times \dfrac{1}{7}\)

\(\dfrac{1}{49}\)

Thus, \(\frac{1}{49}\) is simplified form of the expression \(7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}\).

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119 runners did not finish the race.

To determine the number of runners who did not finish the race, we need to calculate the total number of runners who started the race and subtract the number of runners who finished.

The total number of runners who started the race is the sum of the runners in each wave:

Total runners = Runners in first wave + Runners in second wave + Runners in third wave

Total runners = 341 + 295 + 316

Total runners = 952.

To calculate the number of runners who finished the race, we need to multiply the total number of runners by the fraction of runners who finished (7/8):

Runners who finished = Total runners \(\times (7/8)\)

Runners who finished \(= 952 \times (7/8)\)

Runners who finished = 833.

Since we cannot have half of a runner, we round down the decimal to the nearest whole number since we're dealing with people.

Therefore, 833 runners finished the race.

To find the number of runners who did not finish, we subtract the number of runners who finished from the total number of runners:

Runners who did not finish = Total runners - Runners who finished

Runners who did not finish = 952 - 833

Runners who did not finish = 119

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Answer:

Total people international traveler on cruises = 1,425 million people

Step-by-step explanation:

Given:

Total people international traveler on cruises = 28.5 million

Percentage of international traveler = 2%

Find:

Total people international traveler on cruises

Computation:

Total people international traveler on cruises = 28.5 million × [100/2]%

Total people international traveler on cruises = 1,425 million people

The number of international travelers in 2018 was 570000.

Percentage is a number or ratio expressed as a fraction of 100. One percent is a hundredth part.

Given that in 2018 28.5 million people went on cruises, and this accounted for 2% of international travelers.

The number of international travelers in 2018 was 570000.

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Answer:

10+5y

Step-by-step explanation:

5(2+y)

distribute

=5(2)+5(y)

simplify

=10+5y

Answer:

89,86,83

Step-by-step explanation:

92-80=12

12÷4=3

80+3=83

83+3=86

86+3=89

The complete arithmetic sequence will be: 92, 89, 86, 83, and 80.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as;

aₙ = a₁ + (n - 1)d

Given; The first term (a₁) is 92 and the fifth term (a₅) is 80.

Then the common difference between the terms will be given as;

a₅ = a₁ + (5 - 1)d

80 = 92 + 4d

-12 = 4d

d = -3

Then the missing terms will be

92, 92 - 3, 92 - 6, 92 - 9, and 92 - 12

92, 89, 86, 83, and 80

Hence, the complete arithmetic sequence will be: 92, 89, 86, 83, and 80.

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The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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Answer:

y = 2x + 3

Step-by-step explanation:

You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.

Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.



The slope is 2. Fill in 2 in place of m in

y = mx + b

y = 2x + b

Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.

y = 2x + 3

Answer:

49030

Step-by-step explanation:

we multiply it by ten so

4903×10=49030

Answer:

280 DB

Step-by-step explanation:

If the sound level of a jet plane is approximately 140 dB, the intensity of the sound of a jet plane is approximately 100dB

Sound level is the intensity to measure the sound. Decibels are used to quantify sound levels.

The sound level of a jet plane is expressed according to the expression given:

β = 10log(I/I0)

Given the following parameters

β = 140dB

I0 = 10^-12 W/m²

For required Intensity "I" Substitute:-

140 =10log(I/10^-12)

14 = log(I/10^-12)

10^14 = I/10^-12

I = 10^14 * 10^-12

I = 10^2

I = 100dB

Hence if  the sound level of a jet plane is approximately 140 dB, the intensity of the sound of a jet plane is approximately 100dB

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Answer:

if a polynomial of lowest degree p has zeros at x=x1,x2,…,xn x = x 1 , x 2 , … , x n , then the polynomial can be written in the factored form: f(x)=a(x−x1)p1(x−x2)p2⋯(x−xn)pn f ( x ) = a ( x − x 1 ) p 1 ( x − x 2 ) p 2 ⋯ ( x − x n ) p n where the powers pi on each factor can be determined by the behavior of the graph ...

Answer:

112 cm

Step-by-step explanation:

14 x 8 = 112

Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

The reflection of the graph in the x-axis gives the function

g(x) = -x² - 3x - 2

The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.

The vertex of the function is at (-3/2 , -1/4)

The focus is at ( 3/2 , 0 )

The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0

Now when the parabola is reflected along the x-axis we get

the focus at ( -3/2 , 0 )

the vertex is at  (-3/2 , 1/4)

Axis of symmetry remains the same

The directrix becomes 2y-1 =0

The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.

Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2

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Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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Step-by-step explanation:

I just answered this.

we have 2 angles and their connecting side in between that are congruent (identical).

so, it is D. ASA (angle side angle)

just look up the meaning of the acronyms, and it will all be clear and very easy.

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

-2x+2y+3z=0

-2x-y+z=-3

2x+3y+3z=5

---------------

-2x+2y+3z=0

-2x-y+z=-3

---------------- Subtract

3y + 2z = 3 Eqn A

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

-2x-y+z=-3

2x+3y+3z=5

---------------- Add

2y + 4z = 2

6y + 4z = 6 Eqn A times 2

------------------------------------ Subtract

-4y = -4

y = 1

-----------------

z = 0

-------------------

x = 1

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:The union of positives and negatives do not include 0 because 0 is neither positive, nor negative.

Step-by-step explanation:

If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.

It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.

To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.

0-3 interval:

Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:

slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2

pauses [3, 5]:

Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:

slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5

[5–7] Interval:

Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:

slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1

Interval 7 and 9:

Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:

slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5

As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.

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Answer:

i can help with a littel bit of it

Step-by-step explanation:

1. answer

29±95‾‾‾√9

x

=

−

2

9

±

95

i

9

=−0.222222+1.08298

x

=

−

0.222222

+

1.08298

i

=−0.222222−1.08298

x

=

−

0.222222

−

1.08298

i

Find the Solution for:

92+4+11=0

9

x

2

+

4

x

+

11

=

0

using the Quadratic Formula where

a = 9, b = 4, and c = 11

=−±2−4‾‾‾‾‾‾‾‾√2

x

=

−

b

±

b

2

−

4

a

c

2

a

=−4±42−4(9)(11)‾‾‾‾‾‾‾‾‾‾‾‾√2(9)

x

=

−

4

±

4

2

−

4

(

9

)

(

11

)

2

(

9

)

=−4±16−396‾‾‾‾‾‾‾‾‾√18

x

=

−

4

±

16

−

396

18

=−4±−380‾‾‾‾‾√18

x

=

−

4

±

−

380

18

The discriminant 2−4<0

b

2

−

4

a

c

<

0

so, there are two complex roots.

Simplify the Radical:

=−4±295‾‾‾√18

x

=

−

4

±

2

95

i

18

=−418±295‾‾‾√18

x

=

−

4

18

±

2

95

i

18

Simplify fractions and/or signs:

=−29±95‾‾‾√9

x

=

−

2

9

±

95

i

9

which becomes

=−0.222222+1.08298

x

=

−

0.222222

+

1.08298

i

=−0.222222−1.08298

2. Answer:

=−38±895‾‾‾‾√40

x

=

−

3

8

±

895

i

40

=−0.375+0.747914

x

=

−

0.375

+

0.747914

i

=−0.375−0.747914

x

=

−

0.375

−

0.747914

i

3. Answer:

=0=−74

x

=

0

x

=

−

7

4

=0

x

=

0

=−1.75

Find the Solution for

82+14+0=0

8

x

2

+

14

x

+

0

=

0

using the Quadratic Formula where

a = 8, b = 14, and c = 0

=−±2−4‾‾‾‾‾‾‾‾√2

x

=

−

b

±

b

2

−

4

a

c

2

a

=−14±142−4(8)(0)‾‾‾‾‾‾‾‾‾‾‾‾√2(8)

x

=

−

14

±

14

2

−

4

(

8

)

(

0

)

2

(

8

)

=−14±196−0‾‾‾‾‾‾‾√16

x

=

−

14

±

196

−

0

16

=−14±196‾‾‾‾√16

x

=

−

14

±

196

16

The discriminant 2−4>0

b

2

−

4

a

c

>

0

so, there are two real roots.

Simplify the Radical:

=−14±1416

x

=

−

14

±

14

16

=016=−2816

x

=

0

16

x

=

−

28

16

=0=−74

x

=

0

x

=

−

7

4

which becomes

=0

x

=

0

=−1.75

i hope this helps

Answer:

x= 15/9 fl oz

Step-by-step explanation:

 write the such that chemicals are on one side of : and water on the other

   chemical : water

                 1 : 9

x chemical : 15 of water

now we know that

x/1 = 15/9  cross multiply to find x

x= 1*15/9 = 15/9  ≈ 1.67 fl oz

The correct option regarding whether the point (1,3) is a solution to the system of inequalities is given as follows:

C. No, because it is only a solution for the solid line, not the dashed line.

The solution to the system of inequalities is all the points that are in the shaded region, between the two lines.

Point (1,3) is the intersection of the dashed line with the solid line. The fact that the line is dashed means that the it's extremes such as point (1,3) do not belong to the solution of the system of inequalities, meaning that option C is the correct option.

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