KHAN ACADEMY LESSON HELP ME : Two-step inequality word problems

Answer:

A: 25,500

B: 14,600

C: 10,900

Step-by-step explanation:

This is what we know:

a = b + c

a + b + c = 51,000       Substitute in a for b + c

a + a = 51000  Combine like terms.

2a = 51000  Divide both sides by 2

a = 25,500

28a + 16b + 12c = 1078400   Substitute in 25.600 for a

28(25500) + 16b + 12c = 1078400

714000 + 16b + 12c = 1078400  Subtract 714000 from both sides

16b + 12 c = 364400

25500 +b + c = 51000  Subtract 25500 from both sides

b + c + = 25500    Multiply this equation all the way through by -12 and add it to the bold equation above it.

-12b -12c = -306000

16b + 12c = 364400

4b = 58400   divide both sides by 4

b = 14600

a + b + c = 51000  Plug in what we know

25500 + 14600 + c = 51000

40100 + c = 51000  Subtract 40100 from both sides

c = 10900

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]

We rewrite the integrand.

     [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]

We integrate terms by terms:

The integral of the constants have this constant multiplied by the variable of integration.

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]

That u = x -1. Then that du = dx and we put du.

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]

Integral 1/u is log(u). If you now substitute u further into:

              [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]

The integral of the product of a function by a constant is the constant times the integral of this function:

           [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]

Integral 1/u is log(x). Therefore, the result is: -log(x).

The result is: x - log(x) + log(x - 1)

The curved surface area of a cylinder is 24cm²

Given the following data;

Base circumference = 4 cm

Height = 6 cm

Suppose that:

Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

Then, the curved surface area of that cylinder is 2πr h

To find the curved surface area (CSA) of the cylinder we have;

CSA of a cylinder = 2πrh

But 2πr = 4 cm

Now Substituting the values into the equation, we have,

CSA of a cylinder = 6 x 4

CSA of a cylinder = 24 cm²

Hence, The curved surface area of a cylinder is 24cm²

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The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .

The  rental car company charges $53 per day to rent a car and $0.08 for every mile driven.

Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.

Therefore, the inequality to represent the total number of days Rashaad can rent  the car can be represented as follows:

Therefore,

53d + 0.08(475) ≤ 250

53d + 38 ≤ 250

53d ≤ 250 - 38

53d ≤ 212

divide both sides of the inequality by 53

53d / 53 ≤ 212 / 53

d ≤ 4

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Answer:

the 4th one

Step-by-step explanation:

because we determined by Pythagorean theorem (the square root of 11)2 + 7 the power of 2 =

(the square root of 60)2 .....square root cancelled by power of 2

11 + 49 = 60

60 = 60

The measures of angles 5 and 3 is 100 degrees.

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.

Therefore,

m∠7 = m∠5 (corresponding angles)

corresponding angles are congruent.

Therefore,

m∠5 = 100 degrees

m∠3 = m∠7(alternate angles)

m∠3 = 100 degrees.

Alternate angles are congruent.

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Answer:

Bucket a would be a darker shade because the white makes bucket b lighter.

The commission amount for sales totaling $15,000 is $600.

From the information, the advertising sales representative has sales totaling $4500 and for these sales, the representative earns a commission of $360.

Therefore, the commission fraction will be:

= Commission / Sales

= 360 / 4500

= 1/25

Therefore, the commission on $15000 will be:

= 1/25 × $15000

= $600

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Answer:

(1) where y = 18 when x = 2.

What is the value of x when y = 36?

= 4

(2) when x is 4, y is 11.

What is the constant of proportionality for this relationship?

= 2.75

(3) What is 34% of 650?

=4.875

(4) 28 7

    16 4

    12 3

=1/4x

(5) Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night.

= 15.6

(6) Over 6.8 months, a tree grew 7.48 inches.

=1.1

(7) A party-size bag of chips contains 15 ounces. This is 750% of the amount in the snack-size bag.

=2

(8) An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.

Which proportion could be used to find the commission amount for sales totaling $15,000?

=360/4500=x/15,000

(9) Brad's dinner bill, including a 16% tip, is $10.44.

= 9

(10) Do the values in the table represent a proportional relationship?

x 2 4 6 8

y 3.2 6.4 9.6 12.8

Select from the drop-down menu to correctly complete the statement.

response - correct

All of the y-values are a constant multiple of the corresponding x-values, so the relationship is proportional.

(11) Molly estimated the width of a poster to be 21 inches. The actual width is 26 inches.

=19.2

(12) Solve for x.

x−9= −5/24

=1 7/8

(13) Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.

=3

(14) Landon is buying a shirt priced at $19.99. The sales tax is 8.5%.

= 21.69

(15) A sprinter ran 100 meters in 15 seconds.

=400

(16) Two gears are connected and rotating at the same time.  The smaller gear completes 3 2/3 rotations every time the larger gear completes 1/3  of a rotation.

=11

(17) Jasmine dumped her box of spare change and found out that she had saved 128 coins. She separated them and counted 48 dimes.

What percent of Jasmine's coins are dimes?

= 37.5

(18) A pair of boots costing $299 is marked down 45%.

= 164.45

(19) Figure 1 is dilated to get Figure 2.

What is the scale factor?

Enter your answer in simplest form in the box.

=5/8

(20) y=5/x Not proportional

       y=5(−2x) Proportional

       y=x/4 Proportional

       y=6x+4 Not proportional

Step-by-step explanation:

Hey here u go i so tired lol completely POOPED God bless  u have a great test

The trigonometric equation 2sin3x - √3 = 0 is  expressed as x = π/9 + 2πn/3,  2π/9 + 2πn/3

A trigonometric equation is defined as an equation involving one or more trigonometric ratios of unknown angles

Given: 2sin3x - √3 = 0

2sin3x - √3 = 0

2sin3x = √3

sin3x = √3/2

3x = sin⁻¹√3/2           (Note: sin⁻¹√3/2 = 60° = π/3 in radian)

3x = π/3, π -3            (Note: sine  is positive in 1st and 2nd quadrant)

3x = π/3, 2π/3

x = π/9, 2π/9

x = π/9 + 2πn/3,  2π/9 + 2πn/3

Therefore, 2sin3x - √3 = 0 can be expressed as x = π/9 + 2πn/3,  2π/9 + 2πn/3

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Answer: 81y^4

Step-by-step explanation:

expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.

The value of tα/2 of the t-test is 2.898

A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2

Given:  n = 18 and a 99% confidence interval

We have to find the critical t value for 99% confidence level and sample size of 18

Degrees of freedom = n - 1 = 17

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.

The value obtained from the table is 2.898

Therefore, tα/2 = 2.898

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Answer:

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.

Step-by-step explanation:

The process of calculation of circumcenter has been given below.

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)

We need to find the length of AB, BC and AC

The length will be obtained in terms of x and y

On solving the equations, we will obtain the value of x and y

The value of x and y is the required coordinate of the circumcenter.

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Answer: $306

Step-by-step explanation:

You can find the answer by multiplying 9 by each of the values.

14 * 9 = 126

20 * 9 = 180

Add these values together and you get 306 !

Answer:

$231

Step-by-step explanation:

3 hours for 70 dollars an hour we multiply 70 by 3

70x3

210

And then to get the 10 percent tip we multiply 210 by .10

210x.10

21

And now we add 210 and 21 to get 231

Hopes this helps please mark brainliest

Answer:

44.63

Step-by-step explanation:

( The heart shape makes two half circles and a square )

1 ) The two half circles together make a whole, so we can first find the area of that circle!

2 ) We can see that the dynamiter is 5in. We can cut this in half to find the radius...

5 ÷ 2 = 2.5

3 ) The area of a circle is found with the equation ( A = πr2 ). We can plug in the radius ( 2.5 ) to find the area...

A = π( 2.5 )2 = 19.635in

4 ) Now that we know the area of the circle we can find the area of the square. To find this we can use the equation ( A = a2 ) where a represents the edge length in this case 5in.

A = ( 5 ) 2 = 25in

5 ) We can now add the area of the circle and the area of the square to get the area of the heart!

19.635 + 25 = 44.63

Hope this helps! :)

The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.

First, let us understand the exponents or power:

A power, or index, is a little floating number that appears next to a number or letter.

It is denoted as a^m.

where a = base number

and m = power or index number.

Some laws of exponents are:

We are given:

8^-3

We can solve as;

8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]

So, 8^-3 = 1 / 8^3.

Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.

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The mean age (nearest year) of all the people in the office is 22.4.

Using this formula to find the mean age

Mean age = Sum of men and women age / Number of men and women

Let plug in the formula

Mean age = ( 12 women × 22 years old)  + (3 men × 24 years old) / 12 women + 3 men

Mean age = 264 + 72 / 12 +3

Mean age = 336 /15

Mean age = 22.4

Therefore the mean age is 22.4.

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Answer:

Graph 1:     y = (-3x/5) + 1

Graph 2:    y = 4

Step-by-step explanation:

Both functions are linear, so we can use a linear equation to model these functions. Using slope-intercept form, "y=mx+b" will be easiest, since the graph is shown.

Graph 1:

(1 - (-2))/(0 - 5) = (1 + 2)/-5 = -3/5 = slope

y-intercept (0, 1)

y = (-3x/5) + 1

Graph 2:

(4 - 4)/(1 - 0) = 0 = slope

y-intercept (0, 4)

y = 0x + 4

y = 4

Answer:

First equation : [tex]y=-\frac{3}{5}x +1[/tex]

Second equation : y = 4

Step-by-step explanation:

We want to write equations for the two given lines in slope intercept form

y = mx + b

Where m = slope and b = y intercept

Identifying the y intercept

First lets find the y intercept.

The y intercepts is where the line passes the y axis.

By looking at the first line it appears that the line passes the y axis at (0,1) meaning the y intercept is 1 so b = 1

Identifying the slope

We can find the slope using the slope formula

slope = (y1-y2)/(x1-x2)
Where the values of x and y derive from any two points on the line. (x1,y1) and (x2,y2)

The points used may vary as there are many options however I have chosen (0,1) and (-5,4)

So (x1,y1) = (0,1) and (x2,y2) = (-5,4)

Meaning x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4

( we now plug these into the slope formula )

Again recall slope = (y1-y2)/(x1-x2)  

==> plug in x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4

slope = (1-4)/(0-(-5))

==> reduce subtraction

slope = -3/5

so our slope(m) is -3/5

Plugging in slope and y intercept into slope intercept form

Finally we plug in the values of m and b into slope intercept form to get the equation

Again we have y = mx + b

m = -3/5 and b = 1

So our equation is y = -3/5x + 1

Identifying equation for second line

When we have a horizontal line our equation is going to be put in y = b form where b = the y value that the line crosses. (or y intercept)

Here the line goes through the y value of 4 so b = 4

Hence, the equation of the second line would be y = 4

Using the addition, the number that shows 2 more count from 6 is 8.

In the given question we have to write the number that shows 2 more.

We have to start counting from 6.

To write the number that shows 2 more we add 2 in 6, then again add 2 in the result of add of 2 and 6 and so on.

Hence the number that shows 2 more starting from 6 is

6+2=8

So the number that shows 2 more is 8.

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Answer:

Step-by-step explanation:

1.935<2.5081<2.58<2.8

∵1.9350<2.5081<2.5800<2.8000

The  largest possible volume of the box is 108000cm^3.

The concept is the concept of

We can represent  the length of the square box as x

we can also represent the  surface of the box as S

we can represent the  height of the square box as y

we can represent the  volume as V= xy

Then since the top of the box is open  and we can equate the material of the box is equal  with surface area of box.

then  S=[x^2 +2xy +2xy]

= x^2 +4xy

Then substitute the value of S we have

10800= x^2 +4xy

y= [10800-x^2/4x]

V=2700 * 1/4X^2

V=2700 * 1/4X^2

Then substitute the value of y into

V= xy

= x[10800-x^2/4x]

V= 2700x - 3/4X^2

Differentiate the volume to 0

=3x^2 = 2700

X^2 = 3600

X = 60 and Y = 30

V=2700 * 1/4X^2

V= 270(60) - 1/4* (60)^2 = 108000cm^3

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Answer:

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

Equation of circle:

The center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.

So the coordinates of the center are:

The equation is:

Answer:

[tex](x+8)^2+(y-8)^2=64[/tex]

Step-by-step explanation:

Required conditions:

If the circle is tangent to both axes, its center will be the same distance from both axes.  That distance is its radius.

If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).

Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.

If the radius is 8 units, then the center is (-8, 8).

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:

[tex]\implies (x-(-8))^2+(y-8)^2=8^2[/tex]

[tex]\implies (x+8)^2+(y-8)^2=64[/tex]

Humberto's displacement is 2 miles due south far from his starting point.

We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.

Displacement, unlike distance, shows the direction and position of an object from its original base.  This means that displacement refers to how far an object has traveled out of its original position with the direction included.

In other words, displacement shows the object's overall change in position and the direction of the new position from the former.

Starting point = 0

Distance covered toward the north = 3 miles

Distance covered toward the south = 5 miles

Displacement = 2 (0 - 3 + 5) miles

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For the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

As given in the question,

For the given graph of quadratic function ,

Given graph represents the parabola.

Standard equation of the parabola with vertex ( h, k) is given by,

y = a ( x - h )² + k

Substitute the value ( h ,k ) = ( 4, 2 )

y = a ( x - 4 )² + 2

As it is a parabola in the first quadrant and faces in the upward direction,

Value of x tends to -∞ to ∞

Domain = ( -∞ , ∞ )

Minimum value of y coordinate is 2 and increases to ∞.

Range = ( 2, ∞ )

Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain  and the range in the interval notation is given by :

Domain = ( -∞ , ∞ )

Range = ( 2 , ∞ )

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Answer: 21

Step-by-step explanation

if the premier is 97 the square value of x is 21

Answer:

It's A.

Step-by-step explanation:

If you subtract from y, the graph moves to the right. If you add, it moves to the left.

Answer:

6

the recurring digit is 6

ANS: 0.6