Which equation can be used to represent the statement?

The sum of one-sixth of a number and negative two is equal to negative two-thirds.
1. One-sixth + n = negative 2 + two-thirds
2. One-sixth + n = negative 2 + (negative two-thirds)
3. One-sixth n + 2 = negative two-thirds
4. One-sixth n minus 2 = negative two-thirds

Answer:

1) 22

2)0.875 ounce

3) 2.25 meters

4) 25 ounces

Step-by-step explanation:

divide 110 by 5

divide 7.20 by 8

divide 11.25 by 5

and divide 625 by 25

Answer: 2

Step-by-step explanation:

Answer:

I think it's 2kg

Step-by-step explanation:

13/5 ÷ 13/10

Reciprocate

13/5 × 10/13

= 26/13

=2kg

Answer:

Yes, correct

Step-by-step explanation:

Hope that helppppps

Answer:5+2=?

absolute value of -5 is 5

absolute value of -2 is 2

Step-by-step explanation:

Answer:

  { 4 }

Step-by-step explanation:

First you need to solve the equation. Then you need to write the solutions as a set.

__

I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...

  { 4 }

__

Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.

  √(5x +16) -2 = 3x -8 . . . . given

  √(5x +16) = 3x -6 . . . . . .  add 2

  5x +16 = (3x -6)^2 . . . . .  square both sides

  5x +16 = 9x^2 -36x +36 . . . . expand the square

  9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form

Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...

  9x^2 -36x -5x +20 = 0

  9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs

  (9x -5)(x -4) = 0

The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...

  √(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9

  3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same

  x = 5/9 is NOT A SOLUTION

__

  √(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4

  3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...

  x = 4 is a solution

The set of solutions is then ...

  { 4 } . . . . . solution set

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation \(t=\frac{k}{p}\)

t is time

k is a constant

p is people

We must substitute the values into the equation

\(54=\frac{k}{9}\)

\(k=486\)

Now we must substitute it to find the time

\(t=\frac{486}{6}\)

you get 81

It would take \(6\) builders  \(36\) days to complete the same house.

Builders are those person whose job is to build or repair houses and other buildings.

We have,

\(9\) builders take \(54\) days to complete a house.

So,

\(1\)  builder will take  \((\frac{54}{9})\)  days to complete a house,

In the same way,

\(6\)  builder will take  \((\frac{54}{9}*6)\)  days to complete a house,

i.e.

\(6\)  builder   \(=(\frac{54}{9}*6)= 36\) days.

Hence, we can say that it would take \(6\) builders  \(36\) days to complete the same house.

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The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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From the given table,

1 Pizza corresponds to 4 students

2 Pizza corresponds to 8 students

3 Pizza corresponds to 12 students

4 Pizza corresponds to 16 students

As you notice, for every pizza there are 4 students,

so the multiplier is 4.

2 pizza x 4 = 8 students

3 pizza x 4 = 12 students

4 pizza x 4 = 16 students

The answer is Option B. Multiply the number of pizza by 4 to find the number of students

Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0

Step-by-step explanation:

f(x)= 1/x+2= (1+2x)/x  ,   x<>0

g(x)=1/x-3=(1-3x)/x    , x<>0

=>f(x)/g(x)= (1+2x)/(1-3x)    ,  x<>0

Answer:

-6

Step-by-step explanation:

6x + y = -1

y = -6x-1

slope which is m is -6

Total earnimgs per hour=10$

After deduction

Total earnings

Total hours:-

Approximately 89 hours

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Simplify the equation first

\(\\ \tt\hookrightarrow y=\dfrac{3}{5}x\)

\(\\ \tt\hookrightarrow y={0.6}x\)

Find slopes one by one

#1

\(\\ \tt\hookrightarrow m=\dfrac{8-4}{6-3}=\dfrac{4}{3}=1.3\)

#2

\(\\ \tt\hookrightarrow m=\dfrac{8-4}{10-5}=\dfrac{4}{5}=0.8\)

#3

\(\\ \tt\hookrightarrow m=\dfrac{36-18}{62-31}=\dfrac{18}{31}=0.6\)

Option C is correct

#4

\(\\ \tt\hookrightarrow m=\dfrac{22-11}{36-18}=\dfrac{11}{18}=\dfrac{0.6111}=0.7\)

#5

\(\\ \tt\hookrightarrow m=\dfrac{14-7}{24-12}=\dfrac{7}{12}=0.5\)

Option E is correct

Answer:

Step-by-step explanation:

We know that:

Let's first convert 3/5 into decimal to avoid confusion.

I will choose the first two points in all the tables. Next, l will use the slope formula to find the slope. Then I will compare the slope with the slope of the given equation. If the statement is false, then it is incorrect. If the statement is true, it is correct. Now, let's verify the slopes of all the options to see which slope is less than 0.6.

________________________________________________

Option A (Verification)

Since the statement is false, this is incorrect.

________________________________________________

Option B (Verification)

Since the statement is false, this is incorrect.

________________________________________________

Option C (Verification)

Since the statement is true, this is correct.

________________________________________________

Option D (Verification)

Since the statement is false, this is incorrect.

________________________________________________

Option E (Verification)

Since the statement is true, this is correct.

________________________________________________

We can now conclude that Option C and E is correct.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Number of car sold are 98.

Number of trucks sold are 66.

Given,

Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .

Let number of cars sold are x.

Let number of cars sold of y .

Now,

For dealership 1 equation will be,

x + y = 164  ......(1)

For dealership 2 equation will be,

As the cars are sold twice and trucks are sold half .

2x + y/2 = 229......(2)

Solving 1 and 2,

y = 66

x = 98

Thus number of car sold are 98.

Thus number of trucks sold are 66.

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Answer:

-0.6, -0.12, -0.024

Step-by-step explanation:

divide 5

Answer:

7 weeks.

Step-by-step explanation:

1000 x 40 = 40000

40000 x 7 = 280000

18000 x 7 = 126000

126000 + 75000 = 201000

280000 - 201000 = 79000

553000 ÷ 79000 = 7

The interval that contains the scalar for this problem is given as follows:

Between -1 and 0.

When a vector is multiplied by a scalar, each component of the vector is multiplied by the scalar.

For this problem, we have that the direction of the vector u changed when it was multiplied by the scalar, hence the scalar is a negative number.

As vector v is smaller than vector u, the scalar has an absolute value that is less than 1, hence the number is between -1 and 0.

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Answer:

C. P–1(t) =   log5 (StartFraction t Over 19,300 EndFraction)

Step-by-step explanation:

The inverse function of P(t) is \(P^{-1} (t)=log_{5}( \frac{t}{19300})\)                    

The inverse function is a function obtained by reversing the given function. An inverse is a function that serves to “undo” another function. The domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.

For the given situation,

The function P(t) = 19,300(5)^t, where t is the elapsed time in hours.

Steps to find inverse function:

Step 1: Replace P(t) as y

\(P(t) = 19,300(5)^t\)

⇒ \(y= 19,300(5)^{t}\)

Step 2: interchange t and y

⇒ \(t = 19,300(5)^y\)

Step 3: Now solve for y

⇒ \(\frac{t}{19300} =5^y\)

By law of logarithm,

\(a^{x} = y\)

⇒ \(log_{a} y=x\)

Thus the equation becomes,

⇒ \(log_{5} \frac{t}{19300}=y\)

Step 4: Now replace y as \(P^{-1}( t)\)

⇒ \(P^{-1} (t)=log_{5}( \frac{t}{19300})\)

Hence we can conclude that the inverse function of P(t) is \(P^{-1} (t)=log_{5}( \frac{t}{19300})\).

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Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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Answer: a carrot

Step-by-step explanation:

The number of inches apart that the four bolts will be along the circumference of the metal plate shown in the figure is 9.425 inches.

The circumference refers to the total distance around a circle.

The circumference can determined using the following formula.

Circumference = 2πr

Diameter of the circle = 12 inches

Radius = 12/2 inches = 6 inches

Circumference = 2 x 22/7 x 6

= 37.7 inches

The number of bolts along the circumference = 4

Distance between the four bolts = 9.425 inches (37.8 ÷ 4)

Thus, using division operation, the distance apart of the four bolts is 9.425 inches.

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To find the perfect square trinomial, we proceed as follows;

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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