Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .

Converting [tex]\frac{10}{6}[/tex] into improper fraction,

[tex]\frac{10}{6}\\\\=\frac{5}{3}[/tex]

Divide 5 by 3, we get 1 with remainder 2

Now, write 1 as whole number , 2 as new numerator  and denominator remains same i.e. 3

Now, Improper fraction is [tex]1\frac{2}{3}[/tex] .

Thus, the improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .

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Answer:

20 gallons

Step-by-step explanation:

2/5 = 4/10

3/10 = 6 gallons

1/10 = 6 : 3= 2 gallons

10/10 = 2 * 10 = 20 gallons

Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.

In the given question we have to simplify the given expression.

The given expression is 1/4(12k-4).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

1/4(12k-4) = 1/4*12k-1/4*4

1/4(12k-4) = 3k-1

Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.

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The selling price of the first washing machine is $300

The selling price of the second washing machine is $336

The first washing machine appear to have more savings in cost

The question is a percentage problem

The first is marked down by ​50%

= 50 percent

= 50 / 100

= 0.5

marked down factor = 1 - 0.5 = 0.5

selling price of the first machine = 600 * 0.5 = 300

Similarly the second selling washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 600 * 0.7 = 420

second mark down

20% = 0.2

marked down factor = 1 - 0.2 = 0.8

selling price of the second washing machine at second mark down

= 420 * 0.8 = 336

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Answer:

Step-by-step explanation:

Peter=x

Phillippa= 3x then x

Palvin= 10 then Phillippa

Step 2: Answer: Phillipa 3x+x+10

The equation that could solve how many hours it will take for the second car to catch up to the first car is 55t = 120 + 40t.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

If the first car is going 40 mi/h, and has a 120 mile head start, then the distance it covers at time = t is,

d1 = 120 + 40t

If the second car is going 55 mi/h, you want to know the amount of time it will catch the first car, then, their distance must be equal.

d2 = 55t

d1 = d2

120 + 40t = 55t

Simplify the equation of t.

55t - 40t = 120

15t = 120

t = 8

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There are no values within the interval that satisfies the condition stated by Rolle's theorem.

In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:

f'(c) = [f(b) - f(a)] / (b - a), where a < c < b

Where:

First, evaluate the function f(x) at x = - 4:

x = - 4

f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8

f(- 4) = - 64 - 64 + 64 + 8

f(- 4) = - 56

Second, evaluate the function f(x) at x = 4:

x = 4

f(4) = 4³ - 4 · 4² - 16 · 4 + 8

f(4) = 64 - 64 - 64 + 8

f(4) = - 56

Third, determine the first derivative of the function f(x) and evaluate it at x = c:

f(x) = x³ - 4 · x² - 16 · x + 8

f'(x) = 3 · x² - 8 · x - 16

x = c:

f'(c) = 3 · c² - 8 · c + 16

Fourth, find the roots of the quadratic function found in the previous step.

3 · c² - 8 · c + 16 = 0

In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.

Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.

Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.

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One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.

To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.

When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.

However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.

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The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.

It should be noted that place value is used to know the value of the numbers that are given in a data.

In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:

= 25 × 1000

= 25000

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The number of teams in the field hockey championship tournament is 16.

The total number of matches played in the field hockey championship are 120 matches.

Each pair of team played one match with each other.

So, let us say that there are N teams in the tournament.

So, we can chose any two teams for a match,

So, applying the permutation formula,

ⁿC₂ = 120

Solving further,

N!/2!(N-2)! = 120

N(N-1)/2 = 120

N(N-1) = 240

On observing closely and applying hit and trial method,

16(15) = 240

So, the values of N is 16.

Hence, 16 teams participated in the tournament.

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Bruce paid $17 and $55 respectively for each of the books

From the question, we have the following statements:

Represent the books with the variables x and y

So, we have the following equations

x = 4 + 3y

x + y = 72

To start with;

We can substitute 4 + 3y for x in the equation x + y = 72

So, we have the following representation

4 + 3y + y = 72

Evaluate the like terms

4 + 4y = 72

Collect the like terms in the above equation

So, we have the following equation

4y = 72 - 4

Evaluate the like terms

4y = 68

Divide both sides by 4

So, we have

y = 17

Recall that x = 4 + 3y

Substitute 17 for y in the equation x = 4 + 3y

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the books are $17 and $55

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Possible question

Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.

What is the cost of each book

The slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following equation -

2x - 12y = - 120

Rearranging the equation, we get -

2x - 12y = 120

12y = 2x - 120

6y = x - 60

y = (1/6)x - 10

The slope of the line perpendicular to the line 2x - 12y = 120 will be -

m[2] = -1 / (1/6) = - 6

m[2] = - 6

Therefore, the slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

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The time it would take for light to travel from Earth to the moon is; 1.28 seconds.

It follows from the task content that the time it would take for light to travel from Earth to the Moon is to be determined.

Since the given speed of light is; 3 × 10⁵ km/s and the distance is; 3.84 × 10⁵ km.

It follows from the formula;

Speed = Distance / Time

Time = Distance/Speed

Time = 3.84 × 10⁵ / 3 × 3.10⁵

Time = 1.28 seconds.

Therefore, the required time it would take to travel from Earth to the moon is; 1.28 seconds.

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The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)

Given equation y = 3x + a / 2x - 5

= y(2x - 5) = 3x + a

= 2xy - 5y = 3x + a

= 2xy - 3x = a - 5y

= x(2y-3) = a - 5y

Hence, x = (a - 5y) / (2y - 3)

First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).

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The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.

The three sides of the triangle are-

h = 24 ft, k = 21 ft, and p = 13 ft.

s = ( 24 + 21 + 13 ) / 2

s = 29

s - a = 29 - 24 = 5

s - b = 29 - 21 = 8

s - c = 29 - 13 = 16

Put in the formula,

Area = √s(s−a)(s−b)(s−c)

A = √ 29 x 5 x 8 x 16

A = 136.23

Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.

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The number of different sequences of stops that the driver can make is 24.

Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:

n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:

= n! / (n – r)!

= 4!

= 4 × 3 × 2

= 24 stops.

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Step-by-step explanation:

we have 11k + 4k.

this is like saying "I have 11 apples and then get 4 more apples - how many apples do I have ?"

in other words, how many "k" do I have ?

11 + 4 = 15.

we have 15k.

and then there is -3 + 8 = 5

so, the answer is

15k + 5

Answer:

15k + 5

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 11k - 3 + 4k + 8

Let's simplify the expression,

→ 11k - 3 + 4k + 8

→ 11k + 4k - 3 + 8

→ (11k + 4k) + (-3 + 8)

→ (15k) + (5)

→ 15k + 5

Hence, the answer is 15k + 5.

26.2% is the total percent of discount offered by the merchant.

Let us assume that each item is $100.

As it is given that 18% is off, we have an amount after off is:

Amount after 18% off = 100 × (100 - 18)/ 100

                           = 100 × 0.82

                           = 82

Next, there is 10% off

So the amount become = 82 ×( 100 - 10) / 100

                                        = 82 ×0.9

                                        = 73.8

So the final price of an item is $73.8

The discount = (100 - 73.8) / 100

                      = 26.2%

Therefore the total percent of discount is 26.2%.

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Answer:

-2/3

Step-by-step explanation:

y2-y1/x2-x1

2-4/2-(-1)

-2/2+1

-2/3

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Answer:

Zyndy is 14, Vyndel is 7.

Step-by-step explanation:

Let Zyndy's age be represented by 'z', and Vyndel's age be represented by 'v'.

Zyndy is twice the age of Vyndel, so z=2v

The sum of their age is twenty-one, so z+v=21

Sub the first equation above into the second to get:

2v+v=21

3v=21

v=7

Knowing v=7, we can say z=2(v)=14.

If maggie owes billy $14, her mother $45 and her sister $32. if Maggie has $100 in her purse and pays everyone back then 9 is the money maggie have left over

Two or more expressions with an Equal sign is called as Equation.

Given,

maggie owes billy $14

Maggies mother $45

Maggies sister $32

Maggies  has $100 in her purse and pas everyone bills, we need to find how much money will maggie have left over

To do this we have to add all the bills and subtract from 100

Fourteen plus forty five plus thirty two

14+45+32

Ninety one

91

Now subtract 91 from 100.

100-91

9

Hence, $9 is the money will maggie have left over

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The area of the shape is 32  square yards

The given consist of one rectangle and a right triangle

The area of the figure = The area of the rectangle + The area of the right triangle

The area of the rectangle = The length × The width

The length of the rectangle = 6 yards

The width of the rectangle = 4 yards

The area of the rectangle = 6×4

= 24 square yards

The area of the triangle = (1/2)bh

The base of the triangle = 9 - 5 = 4 yards

The height = 4 yards

The area = (1/2)× 4 × 4

= 8 square yards

The area of the figure = 24 + 8

= 32 square yards

Hence, the area of the shape is 32  square yards

The complete question is:

What is the area of the shape below?

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Answer:

4√3 (about 6.9) cm.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Here, the length of the longer leg is 4√3, or about 6.9, cm.

Answer:

0 + 0.30 + 0.08

Step-by-step explanation:

hope it helps :)

The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is  z = 3x - 108y - z + 241 = 0.

In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)

where  f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .

Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).

In the case of z₀, evaluation of the given function gives us z = -80.

The partial derivatives are thus-

δf(x,y) / δx = fₓ (x, y) = 3x²

fₓ (x₀, y₀) = fₓ (1, 3) = 3

δf(x,y)/δxy= fᵧ (x, y) = -4y³

fᵧ (x₀, y₀) = fᵧ (1, 3) = -108

Now, arranging these values in equation (i) we obtain:

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)

z +80 = 3x² (x -1) - 4y³ (y - 3)

z = -80 +3x² (x -1) - 4y³ (y - 3)

Now, we will substitute the values of the partial derivatives at the given point:

z = -80 + 3x² (x -1) - 4y³ (y - 3)

z = 3x² (x -1) - 108 (y - 3)

z = 241 + 3x -108y

i.e., 3x - 108y - z + 241

Thus, the correct equation is 3x - 108y - z + 241.

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The complete question is-

A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).

(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.

(b) What is the correct equation for the tangent plane? z=

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The equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.

What is an equation of a line?

A line's equation is a single representation of all of the line's points. The general form of a line equation is ax + by + c = 0, and each point on the line satisfies this equation. The slope of the line and a point on the line are the two necessary components to create the equation of a line.

The equation of a line, in the slope-intercept formula:

y = mx + b

In which,

           m is the slope, that is, how much y changes when x changes by 1.

           b is the y-intercept, that is, the value of y when x = 0.

           Given two points (x,y), the slope is the change in y divided by the change in x.

We have points (-1, -2) and (1, -4).

[tex]m = \frac{(-2 - (-4))}{1 - (-1)}[/tex]

m = 1;

Then,

y = 1x + b

Point (-1,-2) means that when x = -1 and y = -2, we use this to find b.

y = 1x + b

-2 = 1(-1) + b

b = -2 + 1

b = -1

Thus,

y = x -1.

Hence, the equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.

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The graph that shows the x- and y-intercepts to graph the equation. y = 1/3x + 1 is added as an attachment

From the question, we have the following equation that can be used in our computation:

y = 1/3x + 1

We set x = 0 to determine the y-intercept

So, we have

y = 1/3 x 0 + 1

Evaluate

y = 1

So, we have

(x, y) = (0, 1)

We set y = 0 to determine the x-intercept

So, we have

0 = 1/3x + 1

Evaluate

1/3x = -1

This gives

x = -3

So, we have

(x, y) = (-3, 0)

So, the intercepts are (0, 1) and (-3, 0)

See attachment for the graph

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Answer: 27

Step-by-step explanation:

Well we already know that n is 12 and d is 15

So based on what I see we do n + d which would equal 27.