When multiplying polynomials for a math assignment, Pat found the product to be -4x+8x^2-2x^3+5. He then had to state the leading coefficient of this polynomial. Pat wrote down -4. Do you agree with Pat’s answer? Explain your reasoning.

Answer:

Degree = 1

Step-by-step explanation:

Given:

The differential equation is given as:

[tex]\frac{d^2y}{dx^2}+(\frac{dy}{dx})^2+6y=0[/tex]

The given differential equation is of the order 2 as the derivative is done 2 times as evident from the first term of the differential equation.

The degree of a differential equation is the exponent of the term which is the order of the differential equation. The terms which represents the differential equation must satisfy the following points:

The above differential equation doesn't involve any of the above conditions. The exponent to which the first term is raised is 1.

Therefore, the degree of the given differential equation is 1.

You would use long division to determine that 8/12 = 0.667 approximately. The steps would go something like this

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

Step 1) Write 8 under a long division bar and place 12 to the left and outside the bar

Step 2) Change the 8 into 8.0000 (you can have as many trailing zeros as you want)

Step 3) While 12 doesn't go into 8, 12 does go into 80. So you can think of 8.0 as 80. Ask yourself "how many times does 12 go into 80?". The answer is 6 times because 6*12 = 72 (note how 7*12 = 84 is too big). So we write a "6" above the 8.0000 such that it is above the first "0". So far we have 0.6 as the quotient.

Step 4) Multiply that 6 by 12 to get 72. We write the 72 under the 80 and then subtract to get 80 - 72 = 8. Pull down the second 0 from "8.0000" to change that 8 into 80.

Step 5) We effectively repeat steps 3 and 4 again. So thats why we get another 6 as the next part of the quotient, and why the 6's repeat forever. The only reason why there's a 7 at the end is because of rounding.

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

The long division is shown in the image attachment below. The gridlines are there to show how things line up though when you write out the long division steps (to show to your teacher) you wont use any grid lines.

side note: the fraction 8/12 reduces to 2/3. You divide both top and bottom by the GCF 4. So 8/4 = 2 and 12/4 = 3.

The venue will break even after selling 1000 tickets.

The value will be $70,000 at that point.

Step-by-step explanation:

Given,

Charges of band;

C(x) = 55x+15000

Per ticket charges by Venue = $70

V(x) = 70x

For breaking even,

C(x) = V(x)

[tex]55x+15000=70x\\15000=70x-55x\\15000=15x\\15x=15000[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}=\frac{15000}{15}\\x=1000[/tex]

The venue will break even after selling 1000 tickets.

Putting 1000 in V(x)

[tex]V(1000)=70(1000)\\V(1000)=70000[/tex]

The value will be $70,000 at that point.

Keywords: function, multiplication

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Answer:

The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ year\\ P_1=x\\P_2=11,000-x\\I=\$680\\r_1=4\%=4/100=0.04\\r_2=7\%=7/100=0.07[/tex]

substitute in the formula above

[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]

[tex]680=0.04x+(11,000-x)0.07[/tex]      

solve for x

[tex]680=0.04x+770-0.07x[/tex]

[tex]0.07x-0.04x=770-680[/tex]

[tex]0.03x=90[/tex]

[tex]x=\$3,000[/tex]

so

[tex]\$11,000-x=\$11,000-\$3,000=\$8,000[/tex]

therefore

The amount invested at 4% was $3,000 and the amount invested at 7% was $8,000

in this way ,u can do other as well with the help of protractor...

Answer:

y = 3x - 1

The rate of change of the function is 3.

Step-by-step explanation:

The equation of the linear function through the points (- 2, - 7)and (1,2) will be given by  

[tex]\frac{y - ( - 7)}{- 7 - 2} = \frac{x - (- 2)}{- 2 - 1}[/tex]

⇒ (y + 7) = 3(x + 2)

⇒ y = 3x - 1 (Answer)

Now, the rate of change of the function is the slope of the line i.e. 3. (Answer)

We know the equation of a straight line which passes through the points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] is given by  

[tex]\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}[/tex]

Answer: y = -3x - 5

Step-by-step explanation: since the two lines are parallel, it implies that

m1 = m2. From the equation given,

m1 = -3 , m2 = -3

Substantial for m2 in y = mx + c

We now have

y = -3x - 5 since the new line is not passing through any coordinate.

Answer:

The answer is y=-3x-2

I hope it's not too late;)

Step-by-step explanation:

Alejandro read 4 pages in 6 minutes, then it would take him 9 minutes to read 6 pages

Solution:

Given that Alejandro read 4 pages in a book in 6 minutes

Therefore,

4 pages = 6 minutes

Let us find the time taken to read 1 page

time taken to read 1 page = time taken to read 4 pages divided by 4

[tex]\text{ time taken to read 1 page } = \frac{6 minutes}{4} = \frac{3}{2} minutes[/tex]

Thus to read 6 pages at this rate, multiply time taken to read 1 page by 6

[tex]\rightarrow \frac{3}{2} \times 6 = 9[/tex]

Therefore it would take 9 minutes to read 6 pages

The diameter of circle is 1.018 mm.

Step-by-step explanation:

Given,

Circumference of circle = 3.2 mm

We know that;

Circumference = 2πr

[tex]3.2=2\pi r\\[/tex]

Putting π=22/7

[tex]3.2=2*\frac{22}{7}*r\\3.2=\frac{44}{7}r[/tex]

Multiplying both sides by 7/44

[tex]\frac{7}{44}*3.2=\frac{7}{44}*\frac{44}{7}r\\\\\frac{22.4}{44}=r\\\\r=0.509[/tex]

Diameter = 2r

Diameter = 2*0.509

Diameter = 1.018 mm

The diameter of circle is 1.018 mm.

Keywords: circle, circumference

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Answer:

4x+12

Step-by-step explanation:

An expression is a mathematical sentence that doesn't end in an equal sign. This question is asking for you to find four times as much as 12, but doesn't explain what number or phrase you need to find it for. We would replace the unknown number with the variable X.

I may be confusing this with another subject, so sorry if I am! Hope this helps!

The expression  which represents 4 times as much as 12 is,  [tex]4x=12[/tex]

Let us consider that number is x.

Since, 4 times of number is equal to 12.

So that,       [tex]4*x=12\\\\4x=12[/tex]

Hence, the expression  which represents 4 times as much as 12 is,  [tex]4x=12[/tex]

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Answer:

The plot of land was sold for rs 129,600

Step-by-step explanation:

The cost of the plot of land                  =  rs 108,000

Profit calculation ( 20% x 108,000)      =  rs 21,600

Price land was sold                               = (108,000 + 21,600) = 129,600

Answer:

2K + 12L ≥ 87 and 1.5K + 8L > 63

Step-by-step explanation:

It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square  feet of paper to make a lamp.

If K denotes the number of kites that Min-Young made and L denotes the number of lamps she made then  

2K + 12L is the number of wooden sticks that she used which is greater than equal to 87

i.e. 2K + 12L ≥ 87 ........ (1)

Again, 1.5K + 8L is the number of square feet of paper that she used which is greater than 63 sq. feet

i.e. 1.5K + 8L > 63 ........... (2)

Hence, inequalities (1) and (2) are the required answer. (Answer)

Answer:

1) 2K + 12L ≥ 87

2) 1.5K + 8L > 63

Step-by-step explanation:

Answer:

degree = 6

Step-by-step explanation:

Given [tex]f(x)=3x^2[/tex], and [tex]g(x)=4^3+1[/tex], we can find the composition of functions: [tex]fog(x)[/tex] by applying the definition of composition and performing the needed algebra.

Recall that the composition of functions is defined as: [tex]fog(x)=f(g(x))[/tex], where we use as input for the function f(x) the actual expression in terms of "x" of the function g(x):

[tex]f(g(x))=f(4x^3+1)\\f(g(x))=3(4x^3+1)^2\\f(g(x))=3\,(4x^3+1)\,(4x^3+1)\\f(g(x))=3\,[16x^6+4x^3+4x^3+1]\\f(g(x))=3\,[16x^6+8x^3+1]\\f(g(x))=48x^6+24x^3+3[/tex]

Therefore, the degree of this expression is "6" (the highest power at which the variable "x" appears)

Answer:

the answer is 6

Step-by-step explanation:

don't have one

|12x + 1| = 10

Remove the absolute value term and make two equations:

12x +1 = 10

12x +1 = -10

Now solve for both x values:

12x +1 = 10

Subtract 1 from both sides:

12x = 9

Divide both sides by 12:

x = 9/12

12x +1 = -10

Subtract 1 from both sides:

12x = -11

Divide both sides by 12:

x = -11/12

The answer would be (-11/12, 912)

Answer:

[tex]\frac{9}{4}[/tex] or [tex]2\frac{1}{4}[/tex] or [tex]2.25[/tex]

Step-by-step explanation:

1 cm = 25000cm = 1/4 km. 9*1/4=9/4=2 1/4= 2.25

Question:

A computer can sort x objects in t seconds, as modeled by the function below:

t=0.005x^2+0.002x

How many objects are required to keep the computer busy for exactly 9 seconds?

Round to the nearest whole object.

Answer:

42 objects are required to keep the computer busy for exactly 9 seconds

Solution:

Given function is:

Computer can sort x objects in t seconds, as modeled by the function below:

[tex]t = 0.005x^2+0.002x[/tex]

We have to find number of objects required to keep the computer busy for exactly 9 seconds

Therefore t = 9

Substitute t = 9 in given function

[tex]9 = 0.005x^2+0.002x\\\\0.005x^2+0.002x - 9 = 0[/tex]

Let us solve the above equation by quadratic formula,

[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Using the above formula,

[tex]\text{ for } 0.005x^2+0.002x - 9 = 0 , \text{ we have } a = 0.005 ; b = 0.002 ; c = -9[/tex]

Substituting the values of a = 0.005 ; b = 0.002 ; c = -9 in above quadratic formula we get,

[tex]\begin{aligned}&x=\frac{-0.002 \pm \sqrt{0.180004}}{0.01}\\\\&x=\frac{-0.002 \pm 0.4242}{0.01}\\\\&x=\frac{-0.002+0.4242}{0.01} \text { or } x=\frac{-0.002-0.4242}{0.01}\\\\&x=42.22 \text { or } x=-42.62\end{aligned}[/tex]

Ignoring negative value,

x = 42.22 ≈ 42

Thus 42 objects are required to keep the computer busy for exactly 9 seconds

Answer:

339 R11

Step-by-step explanation:

8,147 ÷ 24 = 339 R11

Answer:

C. $792.00

Step-by-step explanation:

33 hours Fred can serve 33 x 6 = 198 tables

minimum gratuity : 3.08 x 198 = 609.8

maximum : 5.23 x 198 = 1035.5

Therefore $792.00 is a reasonable amount

The amount of wax needed to create one set of candles is 84.75 cubic inches.

A cylinder is a 3-D figure that has a radius and a height.

The volume of a cylinder is given as πr²h.

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume.

= 3.14 x 2 x 2 x 5

= 62.8 cm³

We have,

Let's calculate the volume of each candle and then add them together to find the total wax needed for one set of candles.

For the smallest candle, the radius is 0.5 inches and the height is 3 inches, so the volume is:

V1 = π x (0.5)² x (3) = 0.75π cubic inches

For the medium-sized candle, the radius is twice as big, or 1 inch, and the height is twice as big, or 6 inches. So the volume is:

V2 = π x (1)² x (6) = 6π cubic inches

For the largest candle, the radius is three times as big, or 1.5 inches, and the height is three times as big, or 9 inches.

V3 = π x (1.5)² x (9) = 20.25π cubic inches

To find the total wax needed for one set of candles, we add up the volumes:

V (total) = V1 + V2 + V3

= 0.75π + 6π + 20.25π

= 27π cubic inches

= 27 x 3.14

= 84.78 cubic inches

Therefore,

The amount of wax needed to create one set of candles is 84.75 cubic inches.

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Answer:

Its 126 i think

Step-by-step explanation:

Answer:

C) x=126

Step-by-step explanation:

Answer:

Hope I helped!

Step-by-step explanation:

To construct a parallel line, set the compass to the same opening used for the first arc and draw an arc from point G that intersects line GD. This creates a parallel line to line EF through G.

To construct a line parallel to EF through point G, Francis should set the compass point on G and adjust the compass to the same opening that was used to construct the first arc. He then needs to create an arc that intersects GD on the opposite side of point A and extends to the right of point G. This step ensures that the line through G will have the same angle with GD as EF does with GD, allowing it to be parallel to EF.

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Answer:

x^2 - 6x + x - 6

= x^2 - 5x - 6

Answer:

150

Step-by-step explanation:

60 minutes in 1 hour

3x10= 30 in one hour

30x5=150 30 trucks in 5 hours

Tarzan can load 150 trucks in 5 hours.

To calculate how many trucks Tarzan can load in 5 hours based on the rate that he loaded 3 trucks in 6 minutes. First, we convert 5 hours into minutes to match the units of the given rate. There are 60 minutes in 1 hour, so 5 hours is 300 minutes (5 hours x 60 minutes/hour). Next, we need to find out how many 6-minute intervals there are in 300 minutes, which is 300 minutes / 6 minutes/intervals = 50 intervals. Since Tarzan loads 3 trucks per interval, we multiply the number of intervals by the number of trucks per interval to get the total number of trucks loaded in 5 hours: 50 intervals x 3 trucks/interval = 150 trucks.

Answer: 8 ft and 4 in, 8 1/3 ft

Step-by-step explanation:

100/12=50/6=25/3=8.3333333...

1/3 of a foot is 1/3x12 which is 12/3 which is 4 in.

Final answer:

100 inches is equal to 8 feet and 4 inches or 8.33 feet.

Explanation:

To solve this problem, you can convert 100 inches to feet using the unit equivalence:

1 foot = 12 inches

Multiply the number of inches by the unit equivalence:

100 inches ÷ 12 inches per foot = 8 feet and 4 inches

Answer:

50

Step-by-step explanation:

150 divided by 3 is 50 and since you shared only one third the answer will be 50

Answer:50

Step-by-step explanation:

One third equals 1/3 of 150

1/3 ×150 =50

You would pay $5.54 on that item.

Step-by-step explanation:

Given,

Cost of item = $63

Sales tax rate = 8.8%

Amount of sales tax = 8.8% of cost of item

Amount of sales tax = [tex]\frac{8.8}{100}*63[/tex]

Amount of sales tax = [tex]\frac{554.4}{100}[/tex]

Amount of sales tax = $5.54

You would pay $5.54 on that item.

Keywords: percentage, division

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Answer:

[tex]L=\frac{15}{16}\ yd[/tex]

Step-by-step explanation:

The correct question is

Devon needs a wood board with an area of 5/16 square yard to complete a project. If the wood board is 1/3 yard wide, how long must the board be?

we know that

The area of a rectangle is equal to

[tex]A=LW[/tex]

where

L is the length

W is the width

we have

[tex]A=\frac{5}{16}\ yd^2\\\\W=\frac{1}{3}\ yd[/tex]

substitute

[tex]\frac{5}{16}=L(\frac{1}{3})[/tex]

solve for L

[tex]L=\frac{5}{16}(3)[/tex]

[tex]L=\frac{15}{16}\ yd[/tex]

The length of the wood board must be approximately 39.69 yards.

To find the length of the board, we need to divide the total area by the width of the board. The area of the board is 516 square yards and the width is 13 yards.

Therefore, the length of the board can be found by dividing 516 by 13.

516 ÷ 13 = 39.69 yards.

So, the board must be approximately 39.69 yards long to complete the project.

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Answer:

Options A and D are correct.

Step-by-step explanation:

The cost y (in dollars) for x ounces of peanuts is represented by the equation

[tex]y=0.23x[/tex]            .... (1)

It means the cost of each ounce of peanuts is $0.23.

The cost y (in dollars) for x ounces of pecans is represented by the equation

[tex]y=0.45x[/tex]            .... (2)

It means the cost of each ounce of pecans is $0.45.

$0.45 > $0.23

It means the cost for pecans is greater than the cost of peanuts. Option B is incorrect.

[tex]\$0.45-\ $0.23=\$0.22[/tex]

The cost for peanuts is $0.22 per ounce less than the cost for pecans. Option A is correct.

Substitute x=8 in equation (1).

[tex]y=0.23(8)=1.84[/tex]

The cost for 8 ounces of peanuts is $1.84. Option C is incorrect.

Substitute x=8 in equation (2).

[tex]y=0.45(8)=3.6[/tex]

he cost for 8 ounces of pecans is $3.60.. Option D is correct.

Answer:

1) [tex]y> \frac{x}{3}+2[/tex] 2) (0,2) 3) The first and second Points must have x coordinate <-6, or y-coordinate  y >2 e.g. (-7,2), (-6,3)

Step-by-step explanation:

1) To Rewrite it as Slope-intercept form, is to isolate the y on the left side and on the right side the rest of the inequality.

[tex]-x+3y>6\Rightarrow 3y>x+6 \Rightarrow y> \frac{x+6}{3}\Rightarrow y> \frac{x}{3}+2[/tex]

2) Since this is a linear inequality the y intercept is given by "b" parameter.[tex]y> mx+b \Rightarrow y> \frac{x}{3}+2 \Rightarrow b=2[/tex]

So the y-intercept is y > 2, coordinate point (0,2). In the graph, we have a dashed line over 2.

3) Since there no choices, the points that satisfy this inequality lie within the green area. We know that the points for this inequality must satisfy  x < -6 or y> 2:

Testing for (-7,2)  for x<-6 ⇒-7 <-6

[tex]-x+3*y>6\\-(-7)+3*2>6\\7+6>6\\13>6\:\\True\\[/tex]

Testing for (-6,3)  for y>2 ⇒3>2

[tex]-x+3*y>6\\-(-6)+3*3>6\\6+9>6\\15>6\:True\\[/tex]