Solve the problem below

The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72

Given,

In the question:

The function is given as :

Consider f(x) = 3x² 30x - 72.

To find the x-intercept(s) and y-intercept of f(x).

Now, According to the question:

f(x) = 3x²× 30x - 72.

f(x) = 90[tex]x^{3}[/tex] - 72

Solve the equation:

90[tex]x^{3}[/tex] = 72

Make the leading coefficient of the variable one

[tex]x^3 = 72/90\\[/tex]

Cross out the common factor

[tex]x^3[/tex] = 4/5

Take the n-th root on both sides:

x = [tex]\sqrt[3]{\frac{4}{5} }[/tex]

To find the y - intercept(s)

f(x) = 3x²× 30x - 72.

Set x = 0

f(0) = 3 × 0 × 30 × 0 - 72

f(0) = - 72

Hence, The x - intercept (s) is x = [tex]\sqrt[3]{\frac{4}{5} }[/tex] and y - intercept (s) is -72

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The value of the functions f(-1), f(2), and f(5) are -2, 4, -2 respectively.

What is the function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). The number of dependent variables for a function is 1 and the number of independent variable for a function is 1.

Given function is:

[tex]f(x)=\left\{\begin{matrix}-2 & \text{if } x \ne2 \\ 4 & \text{if } x=2\end{matrix}\right.[/tex]

The meaning of the above function is when x is not equal 2, then the value of f(x) is -2 and when x is equal 2, then the value of f(x) is 4.

The dependent variable is f(x). The independent variable is x.

So the value of f(-1) is -2 since x = - 1 ≠ 2.

So the value of f(2) is 4 since x = 2.

So the value of f(5) is -2 since x = 5 ≠ 2.

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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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Using the confidence interval, a 95% confidence interval for the mean rate is (4.4206,4.2106).

In the given question, we have to construct a 95% confidence interval for the mean rate.

There is given  interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day.

It is reasonable to assume that the population is approximately normal.

4.754, 4.375, 4.173, 4.678, 4.425, 4.227, 4.126, 4.250, 3.951, 4.197

We find the mean

Mean=4.754+4.375+4.173+4.678+4.425+4.227+4.126+4.250+3.951+4.197/10

Mean=43.156/10

Mean=4.3156

Standard Deviation(S)=√(x−mean)^2/n−1

S=√(4.754−4.3156)^2/10−1

S=√(0.4384)^2/9

S=√0.1922/9

S=√0.02136

S=0.1462

95%=0.95 confidence interval for z is

Z= [tex]z_{\alpha /2,dt}[/tex]

dt=n−1

dt=10−1

dt=9

[tex]\alpha[/tex] = 1−0.95=0.05

[tex]\alpha /2[/tex]=0.05/2=0.025

Z= [tex]z_{0.025,9}[/tex]

Z= 2.262

Confidence interval

CI=Mean±Z× s/√n

CI=4.3156±2.262× 0.1462/√10

CI=4.3156±2.262× 0.1462/3.1623

CI=4.3156±2.262×0.0462

CI=4.3156±0.105

CI=(4.3156+0.105),(4.3156−0.105)

CI=(4.4206,4.2106)

Hence, a 95% confidence interval for the mean rate is (4.4206,4.2106).

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Answer:

c(x) = .19x + 32.50

Step-by-step explanation:

The cost depends on the number of copies.  The x value is the number of copies and the y value is the cost

c(x) = mx + b  We need to find the rate of change.

(50,42) (150.61)  The rate of change is the change in y over the change in x.

The y values are 61 and 42.  The x values are 150 and 50

[tex]\frac{61-42}{150-50}[/tex] = [tex]\frac{19}{100}[/tex] = .19

We also need the y intercept.  We will use the slope of .19 and the x and y values of one of the points. We could use either point, I am going to use the point (50,42)

y = 42

x = 50

m =.19

y=mx + b

42 = .19(50) + b

42 = 9.5 + b  Subtract 9.5 from both sides

32.50 = b

y = mx + b

y = .19x + 32.50 or

c(x) = .19x + 32.50

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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We can see that there are 3,832 yes votes, we did that by using the given ratio.

We know that the ratio of yes votes to no votes was 4 to 3, so from each 7 votes, 4 are yes and 3 are no.

Then if we take the total number of votes, and we multiply it by (4/7), we will get the total number of yes votes.

In this case we know that the total number of votes is 6706, then the number of yes votes is:

(4/7)*6706 = 3,832

There are 3,832 yes votes.

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The groups would 1 x 1000+  2 x 10 + 1 x 1 + 6 x 1/10

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.

Given:

Divide: 5,108 ÷ 5

Now, dividing

   5 | 5108  | 1021.6

        5

   _______

        0 10

            10

        _____

             0 8

                 5

          _____

                 3 0

                 3 0

               ______

                   0

Hence, the groups would 1 x 1000+  2 x 10 + 1 x 1 + 6 x 1/10

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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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2 percentage of the students in the school are enrolled in health .

How do percentages work?

students are enrolled in health = 162

students are enrolled not  in  health = 38

162 + 38 = 200          Add

Total of 100 Students

then ,

200/100            

= 2%

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Answer: x=-y+9

y=-x+9

Step-by-step explanation:

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:

La altura en metros de cada piso es:

3.2 metros

Step-by-step explanation:

1 hectómetro = 100 metros.

1.92 metros = 1.92 * 100 = 192 m

192/60 = 3.2 metros/piso

The value of the trigonometric function Cos61° + Cos45° is 1.192

The given expression is Cos61° + Cos45°

Now, we have :

Cos61° = 0.4848

and Cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = 0.7072

Now, Cos61° + Cos45° = 0.4848 + 0.7072 = 1.192

Trigonometry is a branch of arithmetic that research relationships among side lengths and angles of triangles. the field emerged within the Hellenistic global at some stage in the third century BC from packages of geometry to astronomical research.

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .

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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 y-intercept for the given function is (0, -68).

The given function is f(x)=21x²-31x-68.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (31/42,−6673/84)

Focus: (31/42,−556/7)

Axis of Symmetry: x=31/42

Directrix: y=−3337/42

Plot (0, -68) and (31/42, -6673/84)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

y-intercept is (0, -68).

Hence, the y-intercept for the given function is (0, -68).

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Answer:

6

the recurring digit is 6

ANS: 0.6

Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.

In the given question,

A bag has 2 red, 3 green, and 6 orange balls.

So total number of balls = 2+3+6 = 11

We have to find the theoretical probability.

(a) We have to find the theoretical probability of selecting green ball.

P(G) = Total number of green balls/Total number of balls

P(G) = 3/11

Hence, the probability of selecting green ball is 3/11.

(b) Now we have to find the theoretical probability of not selecting green ball.

Except green ball there is having red and orange i.e.

Total remaining balls except green = 2+6 = 8

P(G) = Total number of balls except green balls/Total number of balls

P(G) = 8/11

Hence, the probability of not selecting green ball is 8/11.

(c) Now we have to find the theoretical probability of selecting orange ball.

P(G) = Total number of orange balls/Total number of balls

P(G) = 6/11

Hence, the probability of selecting green ball is 6/11.

(d) Now we have to find the theoretical probability of not selecting orange ball.

Except orange ball there is having red and green balls i.e.

Total remaining balls except orange = 2+3 = 5

P(G) = Total number of balls except orange balls/Total number of balls

P(G) = 5/11

Hence, the probability of not selecting orange ball is 5/11.

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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]

The slope of the line that passes through the points (1, 6) and (1, 31) is, ∞

Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.

So formula for the slope is,

m = change in y coordinate/change in x coordinate = Δy/Δx = y₂-y₁/x₂-x₁

Given that,

the line passes through the points, (1,6) and (1,31)

So, we can calculate slope for the line by using formula when two are given,

m =  y₂-y₁/x₂-x₁

x₁ = 1

y₁ = 6

x₂ = 1

y₂ = 31

m = 31-(6)/1-1

m ≈ ∞

Therefore, The line is parallel to y-axis

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Answer:

-1

Step-by-step explanation:

Take -1 as common form the denominator then cancel out the whole term i.e x²-x-1 and -1 remains.

The solution to the system of linear inequalities -2x + y ≥ -3 and y > 1/3x + 2 is (3, 3)

In this case, the system of inequalities is given as

-2x + y ≥ -3

y > 1/3x + 2

Next, we plot the graph of the system of inequalities

In this case, the point of intersection of the inequalities represent the solution to the system

From the graph, the lines intersect at (3, -3)

Hence, the solution is (3, 3)

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We solved the system of equations graphically by graphing both equations and identifying the intercept.

The solution is:

(2.41, -1.03)

Here we have only one system of equations, which is:

-x²*y = 6

-x + 2y⁶ = 0

There are multiple ways of solving this, for example, we could isolate the variable "y" on the first equation:

y = -6/x^2

And replace that in the second equation, so we have an equation that only depends on x, but there is an easier way.

We can just graph both equations on the same coordinate axis and see in which points do the graphs intercept. Each intercept will be a solution of the system.

The graph can be seen below, there we can see that the only intersection point is at (2.41, -1.03), so that is the solution of the system.

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The range of six numbers is 8

According to the question,

Total number of Number = 6

Mean of number = 8

Ratio of numbers = 1 : 1 : 2 : 2 : 3 : 3

Let the common factor in numbers be "x"

Then , sum of number will be x + x + 2x + 2x + 3x +3x

=> 12x

Mean = sum of quantity / Number of quantity

8 = 12x / 6

Calculating the value of x,

12x = 48

=> x = 4

Substituting the value of x,

Number will be : 4 , 4 , 8 , 8, 12 , 12

Range = highest number - smallest number

Here , highest is 12 and smallest is 4

Therefore , Range = 12 - 4

=> 8

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We could finish this question by applying the linar programming concept.

The profit function for the business is P(x) = 7x - 161

The number of units must be produced for the business to break even is

To find the formula of profit function, we have to understand first that profit is the remaining of revenue after being reduced by costs. Hence we could write this equation:

Profit = Revenue - Costs

Profit = R(x) - C(x)

If we create a new function P(x) that represent profit function, hence we could rewrite the profit function into:

P(x) = R(x) - C(x) ... (i)

Based on the question, we have both revenue and costs formulas as stated below:

R(x) = 24x ... (ii)

C(x) = 17x + 161 ...(iii)

We could subtitute equations (ii) and (iii) into equation (i) to get the profit formula:

P(x) = R(x) - C(x)

P(x) = 24x - (17x+161)

P(x) = 7x - 161 ... (iv)

To get the units must be produced, we have to understand that Break Even is a condition where the revenue is exactly the same of its costs, or when the profit is 0 (zero). Hence we could write the equation:

P(x) = 0 ...(v) --> Break Even

Then we would subtitute the equation (iv) into equation (v) to find the units must be produced (x) to achieve the break even.

P(x) = 0

7x - 161 = 0

7x = 161

x = 23 ... (vi)

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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 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:

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

Answer:

AAS

Step-by-step explanation:

Two angles and two sides are marked as congruent.  Vertical angles are congruent, so the answer is  AAS