Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate the AREA of the blanket if x = 2.

Write A Polynomial Expression, In Simplified Form, That Represents The AREA Of The Blanket And Use The
Write A Polynomial Expression, In Simplified Form, That Represents The AREA Of The Blanket And Use The

Answers

Answer 1

Answer:

Polynomial expression that represents the area of blanket:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex]

If [tex]x=2[/tex]: [tex]A(2)=13cm^2[/tex]  

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

[tex]A=lw[/tex]

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

[tex]l=(3x+7)cm[/tex]

[tex]w=(2x-3)cm[/tex]

Substitute them into  [tex]A=lw[/tex]:

 [tex]A(x)=(3x+7)(2x-3)[/tex]

Then:

Use Distributive property (Remember the Product of powers property: [tex]b^a*b^c=b^{(a+c)}[/tex] ):

[tex]A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21[/tex]

Add like terms:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex] (Simplied form)

Evaluate [tex]x=2[/tex]:

[tex]A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2[/tex]


Related Questions

Mason has to mow 6 lawns today. So far, he has mowed 1 1/2 of them. How many does he have left to do?
2 1/2
3 1/2
4 1/2
7 1/2

Answers

4 1/2. Take six minus 1 1/2 and you will get 4 1/2

When 9^2/3 is written in simplest radicsl form, which value remains under the radical? 3 6 9 27

Answers

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 9^{\frac{2}{3}}\implies (3^2)^{\frac{2}{3}}\implies 3^{2\cdot \frac{2}{3}}\implies 3^{\frac{4}{3}}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}[/tex]

Answer:

\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 9^{\frac{2}{3}}\implies (3^2)^{\frac{2}{3}}\implies 3^{2\cdot \frac{2}{3}}\implies 3^{\frac{4}{3}}\implies \sqrt[3]{3^4}\implies \sqrt[3]{3^3\cdot 3^1}\implies 3\sqrt[3]{\stackrel{\textit{this one}}{3}}

Step-by-step explanation:

A satellite is in a approximately circular orbit 36,000 kilometers from Earth's surface. The radius of earth is about 6400 kilometers. What is the circumference of the satellite's orbit?

Answers

Answer:  [tex]266,407.057\ km[/tex]

Step-by-step explanation:

The formula used to calculate the circumference of a circle is:

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

The radius of the circle is r.

In the diagram you can observe that the radius of the satellite's orbit (r2) is the sum of the radius of the Earth (r1) and the distance from the Earth's surface to the satellite's orbit:

[tex]r2=r1+36,000\ km\\r2=6,400\ km+36,000\ km\\r2=42,400\ km[/tex]

Then, the circumference of the satellite's orbit is:

[tex]C=2\pi (42,400\ km)\\C=266,407.057\ km[/tex]

Final answer:

The circumference of the satellite's orbit is calculated by adding Earth's radius to the satellite's distance from Earth's surface to determine the orbit radius. The circumference is then found by using the formula for the circumference of a circle, 2πr, giving approximately 266,433 kilometers.

Explanation:

To find the circumference of the satellite's orbit, we need to first calculate the total distance from the center of Earth to the satellite. This is the sum of the Earth's radius (6400 kilometers) and the satellite's distance from the Earth's surface (36000 kilometers), which totals 42400 kilometers.

Once we have the radius of the orbit, we can calculate the circumference using the formula for the circumference of a circle, which is 2πr (two times Pi times the radius). Using this formula, the circumference of the satellite's orbit is approximately 266,433 kilometers.

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Liam has 2 quarts of apple juice. He wants to pour the juice into 1/5-quarts servings. How many servings can he pour?

Answers

Answer:

10 servings

Step-by-step explanation:

Divide the total juice available, 2 quarts, by the serving size, (1/5) quart per serving:

 2 quarts                     2        5

--------------------------- = ----  ·  ------ servings = 10 servings

(1/5) quart/serving       1         1

A bag contains a white, a red, and a blue marble. If one marble is drawn randomly from a bag, not replaced, and a second marble is drawn, display all possible outcomes as an organized list.

Answers

Final answer:

To answer the student's question, we list each possible pair of marble colors drawn without replacement from a bag with a white, red, and blue marble: White-Red, White-Blue, Red-White, Red-Blue, Blue-White, and Blue-Red.

Explanation:

The question asks for the display of all possible outcomes when two marbles are drawn from a bag containing a white, a red, and a blue marble, without replacement. To show all possible outcomes, we can list them in an organized manner, considering each color once it is drawn, is not put back into the bag. The first marble drawn can be any one of the three colors. Once a marble is drawn, there are only two colors left for the second draw.

White, RedWhite, BlueRed, WhiteRed, BlueBlue, WhiteBlue, Red

PLEASE HELP!! TIMED QUESTION!!!!! WILL AWARD BRAINLIEST!!!!!

If f(x) = x^2 + 3x + 5 , what is f (a + h) ?

A. (a+h)^2 + 3(a+h) + 5(a+h)
B. a^2 + 2ah + h^2 + 3a + 3h + 5
C. h^2 + 3a + 3h + 5
D. (x^2 + 3ax + 5) (a + h)

Answers

the answer is A, what they changed is the (x) with (a+h), so the right side equation should be changed the same way just like A.

Find the inverse of the matrix [tex]\left[\begin{array}{ccc}9&-2\\-10&9\\\end{array}\right][/tex] , if it exist.

Answers

Answer:

The answer is (b)

Step-by-step explanation:

* Lets check how to find the inverse of the matrix,

 its dimensions is 2 × 2

* To know if the inverse of the matrix exist find the determinant

- If its not equal 0, then it exist

* How to find the determinant

- It is the difference between the multiplication of

 the diagonals of the matrix

Ex: If the matrix is [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]

     its determinant = ad - bc

- After that lets swap the positions of a and d, put negatives

 in front of b and c, and divide everything by the determinant

- The inverse will be [tex]\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc}\\\frac{-c}{ad-bc} &\frac{a}{ad-bc}\end{array}\right][/tex]

* Lets do that with our problem

∵ The determinant = (9 × 9) - (-2 × -10) = 81 - 20 = 61

- The determinant ≠ 0, then the inverse is exist

∴ The inverse is [tex]\frac{1}{61}\left[\begin{array}{ccc}9&2\\10&9\end{array}\right][/tex]=

   [tex]\left[\begin{array}{ccc}\frac{9}{61}&\frac{2}{61}\\\frac{10}{61} &\frac{9}{61}\end{array}\right][/tex]

* The answer is (b)

A table is 4 ft high. A model of the table is 6 in. high. What is the ratio of the height of the actual table to the height of the model table?
1/8

8/1

2/3

3/2

Answers

2/3 is the answer because 6 in is the model and 4 ft is the actual

Answer:

The  ratio of the height of the actual table to the height of the model table is [tex]\frac{8}{1}[/tex] .

Step-by-step explanation:

As given

A table is 4 ft high. A model of the table is 6 in. high.

As

1 foot = 12 inch

Now convert 4 ft into inches .

4 ft = 4 × 12

     = 48 inches

Height of the actual table = 48 inches

Now the ratio of the height of the actual table to the height of the model

table .

[tex]Ratio\ of\ the\ height\ of\ the\ actual\ table\ to\ the\ height\ of\ the\ model\ table =\frac{48}{6}[/tex]

[tex]Ratio\ of\ the\ height\ of\ the\ actual\ table\ to\ the\ height\ of\ the\ model\ table =\frac{8}{1}[/tex]

Therefore the  ratio of the height of the actual table to the height of the model table is [tex]\frac{8}{1}[/tex] .

True or false (picture provided)

Answers

False. That does not satify the equation

Answer:

False

Step-by-step explanation:

The given inequality  is [tex]-3 \:<\:x\:<\:14[/tex].

Since both boundaries of the inequalities are not inclusive , we use the parenthesis for open interval."()".

We write the given inequality in interval notation as;

[tex](-3,14)[/tex].

The correct choice is false

Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.

A (5 square root 2, 225°), (-5 square root 2, 45°)

B (5 square root 2, 315°), (-5 square root 2, 135°)

C (5 square root 2, 135°), (-5 square root 2, 315°)

D (5 square root 2, 45°), (-5 square root 2, 225°)

Answers

Answer:

 the answer is B (5 square root 2, 315°), (-5 square root 2, 135°)

Step-by-step explanation:

1) Let A be the point (x, y) = (5, - 5)  

=> x = 5 and y = - 5  

r = √(x² + y²) = √(25 + 25) = √50 = ± 5√2  

tan Θ = - 5/5 = - 1  

=> Θ = (i) 315º or - 45º ; (ii) 135º or - 225  

Hence, the Polar Coordinates of A are (i) (5√2, 315º) (ii) (- 5√2, 135º)

Two pairs of polar coordinates for the point is option b,

Calculation of two pairs:

Here we assume that A be the point (x, y) = (5, - 5)  

So,

x = 5 and y = - 5  

Now

[tex]r = \sqrt(x^2 + y^2) = \sqrt(25 + 25) = \sqrt50 = \pm 5\sqrt2[/tex]

tan Θ = - 5/5 = - 1  

Now

(i) 315º or - 45º ; (ii) 135º or - 225  

So, the polar coordinates should be (5 square root 2, 315°), (-5 square root 2, 135°)

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the value pi/4 is a solution for the equation 3 sqrt 2 cos theta+2=-1

Answers

Answer:

FALSE

Step-by-step explanation:

[tex]3\sqrt2\cos\theta+2=-1\\\\\text{Method 1}\\\\\text{Put}\ \theta=\dfrac{\pi}{4}\ \text{to the equation and check the equality:}\\\\\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\L_s=3\sqrt2\cos\dfrac{\pi}{4}+2=3\sqrt2\left(\dfrac{\sqrt2}{2}\right)+2=\dfrac{(3\sqrt2)(\sqrt2)}{2}+2\\\\=\dfrac{(3)(2)}{2}+2=3+2=5\\\\R_s=-1\\\\L_s\neq R_s\\\\\boxed{FALSE}[/tex]

[tex]\text{Method 2}\\\\\text{Solve the equation:}\\\\3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\\\\3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\\\\\cos\theta=-\dfrac{3}{3\sqrt2}\\\\\cos\theta=-\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\\cos\theta=-\dfrac{\sqrt2}{2}\to\theta=\dfrac{3\pi}{4}+2k\pi\ \vee\ \theta=-\dfrac{3\pi}{4}+2k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\text{It's not equal to}\ \dfrac{\pi}{4}\ \text{for any value of }\ k.[/tex]

Please Help Me!!!

A cone's base has a circumference of 75.36 cm and a height of 18 cm.

What is the volume of the cone?

Use 3.14 for pi, and round your answer to the nearest hundredth if necessary.

Answers

First, lets start with the formula for the volume of a cone

[tex] \frac{1}{3} (\pi \times {r}^{2})h [/tex]

Then lets find the diameter so we can get the radius...

Since we have circumference, all we need to do is use this formula-

[tex] c \div \pi[/tex]

C being circumference, the PI being the 3.14, we plug it in to the formula as the number we have to get the diameter...

[tex]{75.36} \div 3.14[/tex]

And it comes out to...

24.

Now we need to divide it by two to get the radius, and we come up with 12.

Now that we have our radius, we can finally plug in all of the numbers into our original formula...

[tex] \frac{1}{3} (3.14 \times \: {12}^{2} ) \times 18[/tex]

The answer of the entire problem turns out to be... Drum roll please...

2712.96 cubic centimeters.

A driver accelerates when the car is traveling at a speed of 30 miles per hour (i.e., 44 feet per second). the velocity (in feet per second) function is v(t)=44+2.2t . the car reaches the speed of 60 miles per hour (i.e., 88 feet per second) in 20 seconds. then during the 20 seconds the car has traveled

Answers

Assume the car starts at the origin, so that its initial position is [tex]x(0)=0[/tex]. The car's displacement at any time [tex]t[/tex] over the 20 second interval is

[tex]\displaystyle x(0)+\int_0^t(44+2.2u)\,\mathrm du=0+\left(44u+1.1u^2\right)\bigg|_{u=0}^{u=t}=44t+1.1t^2[/tex]

so that after 20 seconds the car has moved 1320 ft.

###

Without using calculus, recall that under constant acceleration, the average velocity of the car over the 20 second interval satisfies

[tex]v_{\rm avg}=\dfrac{v_f+v_i}2[/tex]

and that, by definition, we have

[tex]v_{\rm avg}=\dfrac{\Delta x}{\Delta t}[/tex]

where [tex]v_f[/tex] and [tex]v_i[/tex] are the final/initial speeds of the car and [tex]\Delta x[/tex] is the displacement it undergoes. It starts with a speed of 44 ft/s and ends with a speed of 88 ft/s, so we have

[tex]\dfrac{88\frac{\rm ft}{\rm s}+44\frac{\rm ft}{\rm s}}2=\dfrac{\Delta x}{20\,\rm s}\implies\Delta x=1320\,\mathrm{ft}[/tex]

same as before.

Final answer:

To find the distance traveled by the car during the 20 seconds, we integrate the velocity function and solve for the distance using the given values. The car travels a distance of 1320 feet.

Explanation:

To find the distance traveled by the car during the 20 seconds, we need to calculate the area under the velocity-time graph. The velocity function given is v(t)=44+2.2t. To find the distance, we integrate the velocity function from 0 to 20 seconds:

d = ∫(44+2.2t) dt

Applying integration, we get: d = 44t + 1.1t^2

Substituting the values t=0 and t=20 into the equation, we can find the distance traveled by the car:

d = 44(20) + 1.1(20)^2

Solving this equation, we get d = 880 + 440

So, the car has traveled a distance of 1320 feet during the 20 seconds.

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Find the area of a parallelogram with vertices at A(–9, 5), B(–8, 10), C(0, 10), and D(–1, 5).


A) 40 square units


B) 30 square units


C) 20 square units


D) none of these

Answers

Answer:

It would be A. 40 square units (:

Step-by-step explanation:

Simplify √ 25 please

Answers

Answer:

the answer is 5

Step-by-step explanation:

25/5=5 & 5*5=25

Answer:

The Answer Is 5 because every square number has to equal the number by multiplying by 2 to get your Answer 5 x 5 = 25 which 5 is multiplied 2 times 5 and 5 which gives you your answer 25.

Step-by-step explanation:

Plz Mark Brainliest

T=−2a^2+a+6
N=−3a^2+2a−5 ​
N − T =

Answer is: −a^2+a−11

Answers

Answer:

[tex]\large\boxed{N-T=-a^2+a-11}[/tex]

Step-by-step explanation:

[tex]T=-2a^2+a+6\\N=-3a^2+2a-5\\\\N-T=?\\\\\text{Substitute:}\\\\N-T=(-3a^2+2a-5)-(-2a^2+a+6)\\\\N-T=-3a^2+2a-5-(-2a^2)-a-6\\\\N-T=-3a^2+2a-5+2a^2-a-6\qquad\text{combine like terms}\\\\N-T=(-3a^2+2a^2)+(2a-a)+(-5-6)\\\\N-T=-a^2+a-11[/tex]

The difference between the functions is [tex]-a^2+a-11[/tex]

Given the following expression:

[tex]T=-2a^2+a+6\\N=-3a^2+2a-5[/tex]

We are to take the difference between N and T and this is as shown:

[tex]N - T= -3a^2+2a-5-(-2a^2+a+6)\\Expand\\N - T= -3a^2+2a-5+2a^2-a-6\\\\Collect \ the \ like \ terms\\N-T=-3a^2+2a^2+2a-a-5-6\\N-T=-a^2+a-11[/tex]

Hence the difference between the functions is [tex]-a^2+a-11[/tex]

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PLEASE HELP Complete the table with
integer values of x from 0 to 4. Then graph the function.

Answers

Answer:

y = 1 for the line.

Step-by-step explanation:

All values under y = 1. Surprisingly 1^0 is still 1. So just fill the table in with 1s under y.

I've drawn the line in desmos for you. I'm not sure whether you can extend the question enough to graph a line segment containing these 5 points (which is what I have done) or if you should just submit a graph with 4 points on. If it does not cost you anything to submit it twice, I would try the line first and the points alone the second time.

What angle pair is matched with ∠MLA to make alternate interior angles ?

Answers

angle GAL would be the same as MLA

Karli produces organic cheese from milk supplied by an organic dairy. Karli pays an average of $8.00 for 10 gallons of the organic milk. The direct labor charge of her helper who converts the milk to cheese is $13.00 an hour. Her helper prepares a 5-pound wheel of cheese from 5 gallons of milk, working about 3 hours over several days. To the nearest cent, what is Karli's prime cost of manufacturing a wheel of cheese?

A.34.00
B.17.00
C.48.00
d.43.00

Answers

Answer:

d. $43.00

Step-by-step explanation:

Karli's total cost is ...

total cost = material cost + labor cost

= ($8.00/10 gal)·(5 gal) + ($13.00/h)·(3 h)

= $4.00 + $39.00

= $43.00

135, 131, 127, 123, 119...


1. What is f(1)

2. What is f(6)

3. What is f (26)

4. What is f(n)

Answers

Answer:

[tex]\large\boxed{1.\ f(1)=135}\\\boxed{2.\ f(6)=115}\\\boxed{3.\ f(26)=25}\\\boxed{4.\ f(n)=139-4n}[/tex]

Step-by-step explanation:

[tex]f(1)=135\\f(2)=135-4=131\\f(3)=131-4=127\\f(4)=127-4=123\\f(5)=123-4=119\\\vdots\\\\\text{It's an arithmetic sequence with firs term = 135 and the common}\\\text{difference d = -4.}\\\text{The formula of arithmetic sequence: }\\\\f(n)=f(1)+(n-1)d\\\\\text{We have}\ f(1)=135\ \text{and}\ =-4.\ \text{Substitute:}\\\\f(n)=135+(n-1)(-4)=135+(n)(-4)+(-1)(-4)\\=135-4n+4=139-4n\\\\\boxed{f(n)=139-4n}[/tex]

[tex]\text{Put n = 6, n=26 to the formula:}\\\\f(6)=139-4(6)=139-24=115\\\\f(26)=139-4(26)=139-104=25[/tex]

Find the range and mean of each data set. Use your results to compare the two data sets. Set? A: 13 15 16 18 14 Set? B: 4 10 8 18 20

Answers

Final answer:

The range of Set A is 5 and Set B is 16. The mean of Set A is 15.2 and Set B is 12. Set B has a larger range but a smaller mean compared to Set A.

Explanation:

The range of a data set is calculated by subtracting the smallest value from the largest value. For Set A, the range is 18 - 13 = 5. For Set B, the range is 20 - 4 = 16.

The mean of a data set is calculated by summing all the values and dividing by the number of values. For Set A, the mean is (13 + 15 + 16 + 18 + 14) / 5 = 76 / 5 = 15.2. For Set B, the mean is (4 + 10 + 8 + 18 + 20) / 5 = 60 / 5 = 12.

Comparing the two data sets, we can see that Set B has a larger range than Set A, indicating greater variability in the data. However, Set B has a smaller mean than Set A, indicating that the values in Set B are generally lower than those in Set A.

If r = 11 units and h = 8 units, then what is the volume of the cylinder shown above?

Answers

Answer:

  968π ≈ 3041 . . . cubic units

Step-by-step explanation:

The usual formula for the volume of a cylinder is ...

  V = πr²h

For your given dimensions, the volume is found by putting the values into the formula and doing the arithmetic.

  V = π(11²)(8) = 968π . . . . cubic units

 V ≈ 3041 cubic units

he mean incubation time of fertilized eggs is 23 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. ​(a) Determine the 17th percentile for incubation times. ​(b) Determine the incubation times that make up the middle 97​%. LOADING... Click the icon to view a table of areas under the normal curve. ​(a) The 17th percentile for incubation times is nothing days. ​(Round to the nearest whole number as​ needed.) ​(b) The incubation times that make up the middle 97​% are nothing to nothing days. ​(Round to the nearest whole number as needed. Use ascending​ order.)

Answers

I think a but I’m not quite sure

Identify the horizontal asymptote of f(x) =x2+5x-3/4x-1

Answers

since the numerator is x² + 5x - 3, and therefore has a degree of 2, whilst the denominator, 4x¹ - 1, has a degree of 1, therefore, there's no horizontal asymptote.

recall, we only get a horizontal asymptote if the denominator's expression degree is equals or greater than that of the numerator's.

The function [tex]f(x) = (x^2+5x-3)/(4x-1)[/tex] does not have a horizontal asymptote because the degree of the numerator is higher than the degree of the denominator.

To identify the horizontal asymptote of the function

[tex]f(x) = \frac{{x^2+5x-3}}{{4x-1}}[/tex], you can examine the degrees of the polynomial in the numerator and the polynomial in the denominator. Since the degree of the numerator (which is 2) is higher than the degree of the denominator (which is 1), this function does not have a horizontal asymptote. However, for functions like

[tex]f(x) = \frac{{x^2+3}}{{x^2+4}}[/tex], where the degrees of the numerator and denominator are the same, the horizontal asymptote is determined by the leading coefficients of the numerator and denominator. Specifically, the horizontal asymptote is

[tex]y = \frac{{1}}{{1}}[/tex] = 1,

since the coefficients of the x^2 terms are both 1.

Divide. Write the quotient in lowest terms. 3\dfrac{1}{8} \div 1\dfrac23 = 3 8 1 ? ÷1 3 2 ? =3, start fraction, 1, divided by, 8, end fraction, divided by, 1, start fraction, 2, divided by, 3, end fraction, equals

Answers

By writing the quotient in lowest terms, 3 and 1/8 divided by 1 and 2/3 equals 5 and 5/24.

How to divide the equation

To divide 3 and 1/8 by 1 and 2/3, we can follow these steps:

Step 1: Convert the mixed numbers to improper fractions.

3 and 1/8 = (3 * 8 + 1) / 8 = 25 / 8

1 and 2/3 = (1 * 3 + 2) / 3 = 5 / 3

Step 2: Invert the divisor (the second fraction) and multiply.

25/8 ÷ 3/5 = 25/8 * 5/3

Step 3: Simplify the fractions if possible.

The numerator of 25/8 and the denominator of 5/3 have a common factor of 5.

25/8 * 5/3 = (5 * 25) / (8 * 3) = 125/24

Step 4: Express the improper fraction as a mixed number (if necessary).

125/24 can be expressed as 5 and 5/24.

Therefore, 3 and 1/8 divided by 1 and 2/3 equals 5 and 5/24.

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The solution to [tex]\(3\dfrac{1}{8} \div 1\dfrac23\) is \(\frac{15}{8}\),[/tex] expressed as a fraction in its simplest form after converting the mixed numbers to improper fractions and performing division.

Let's solve [tex]\(3\dfrac{1}{8} \div 1\dfrac23\)[/tex]

convert the mixed numbers into improper fractions:

[tex]\(3\dfrac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8}\)[/tex]

[tex]\(1\dfrac23 = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}\)[/tex]

Now, we have:

[tex]\(\frac{25}{8} \div \frac{5}{3}\)[/tex]

To divide by a fraction, we multiply by its reciprocal:

[tex]\(\frac{25}{8} \times \frac{3}{5}\)[/tex]

Multiply the numerators and denominators:

Numerator:[tex]\(25 \times 3 = 75\)[/tex]

Denominator: [tex]\(8 \times 5 = 40\)[/tex]

Therefore, [tex]\(3\dfrac{1}{8} \div 1\dfrac23 = \frac{75}{40}\)[/tex]

Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5:

[tex]\(\frac{75}{40} = \frac{75 \div 5}{40 \div 5} = \frac{15}{8}\)[/tex]

Hence,[tex]\(3\dfrac{1}{8} \div 1\dfrac23 = \frac{15}{8}\).[/tex]

At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 500 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by about 1 percent. so the number of pounds of grapes produced per acre is modeled by

Answers

Final answer:

The question is about the mathematical modeling of a vineyard's grape production. As the number of vines increases, the individual yield of each vine decreases by 1%. An equation, such as P = 5000 - 50(n-500), is a possible mathematical model to represent this situation.

Explanation:

This question appears to require a detailed understanding of mathematical modeling and percentage decrease concept. The problem presented describes the decrease in grape production per vine as the number of vines planted per acre increases. It's an example of an inverse relationship, when one variable increases the other variable decreases.

The initial production quantity is 10 lb of grapes per vine when there are 500 vines per acre. However, for every additional vine planted, there is a subsequent 1% drop per vine. This means that if 501 vines are planted, each vine then produces only 99% of 10 lbs, or 9.9 lbs, and so on.

To model this mathematically, an equation could possibly be P = 5000 - 50(n-500), where P is the production of grapes in pounds, and n is the number of vines. This formula might help to calculate the maximum yield that could be obtained according to the number of vines.

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Which should you use to find the length of a?

Question 1 options:

Pythagorean Theorem


Law of Sines


Law of Cosines100


Soh-Cah-Toa

Answers

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Pythagoras' theorem is only suitable for right triangles, which this isn't.

The Sine rule would not be applicable as there isn't any side and paired angle given

The best option for this would be the Law of Cosines as it is suitable for when you are given two sides and an angle between the.

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Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

ABC is triangle with its dimensions:

AB = 11

AC = 13

∠A = 108°

BC = a

We need to find the length of 'a'.

So, we can use "Law of cosines" as we have given two sides and one angle.

So, it becomes,

[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}\\\\\cos 108^\circ=\dfrac{11^2+13^2-a^2}{2\times 13\times 11}\\\\-0.3=\dfrac{121+169-a^2}{286}\\\\-0.3\times 286=290-a^2\\\\-85.8=290-a^2\\\\-85.8-290=-a^2\\\\375.8=a^2\\\\a=\sqrt{375.8}\\\\a=19.38[/tex]

Hence, Third option is correct.

If a given data point is (1,4) and the line of best fit is y = 1.5x + 3.25, what's the residual value?

Answers

Answer:

The residual value is -0.75

Step-by-step explanation:

we know that  

The residual value is the observed value minus the predicted value.

RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]

where

Predicted value.--> the predicted value given the current regression equation

Observed value. --> The observed value for the dependent variable.

in this problem

we have the point (1,4)

so

The observed value is 4

Find the predicted value  for x=1

[tex]y =1.5(1)+3.25=4.75[/tex]

predicted value is 4.75

so

RESIDUAL VALUE=(4-4.75)=-0.75

Answer:

-0.75

Step-by-step explanation:

Which equation yields the solutions x=−2 and x=5?

Answers

Answer:

 x² - 3x - 10 = 0

Step-by-step explanation:

Given there are 2 solutions then the equation is a quadratic.

Since the solutions are x = - 2 and x = 5 then

the factors are (x + 2) and (x - 5) and

f(x) = (x + 2)(x - 5) ← expand factors

     = x² - 3x - 10, hence the equation is

x² - 3x - 10 = 0

Final answer:

The equation that yields the solutions x = -2 and x = 5 is: x^2 + 0.00088x - 0.000484 = 0. We can solve this equation using the quadratic formula.

Explanation:

The equation that yields the solutions x = -2 and x = 5 is:

x^2 + 0.00088x - 0.000484 = 0

To solve this equation, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

Plugging in the values from the equation, we get:

x = (-0.00088 +/- sqrt((0.00088)^2 - 4(1)(-0.000484)))/(2(1))

Simplifying further, we have:

x = (-0.00088 +/- sqrt(0.0000007744 + 0.001936))/0.002

Continuing to simplify, we get:

x = (-0.00088 +/- sqrt(0.0027104))/0.002

Finally, we have the two possible solutions:

x = (-0.00088 + sqrt(0.0027104))/0.002 and x = (-0.00088 - sqrt(0.0027104))/0.002

The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. What is the rate of change of the volume of the cylinder when the height is 20cm.

Answers

Answer:

108π cm^3/min

Step-by-step explanation:

At a time of t min, let the height be h cm

The volume of a cylinder;

V = π r^2 h

   = 36π h

differentiating both sides with respect to t;

dV/dt = 36π dh/dt

but dh/dt = 3 cm/min

dV/dt = 36π(3) = 108π cm^3/min

Answer:

The rate of change of the volume of the cylinder when the height is 20 cm is [tex]\frac{dV}{dt}=108\pi \:{\frac{cm^3}{min} }[/tex]

Step-by-step explanation:

This is a related rates problem. In this problem, you need to find a relationship between the quantity whose rate of change you want to find, the volume in this case, and the quantity whose rates of change you know, the height of the cylinder.

We know that the volume of the cylinder is

[tex]V=\pi r^2h[/tex]

We also know that the radius is a constant, 6 cm and thus

[tex]V=\pi (6)^2h=36\pi h[/tex]

V and h both vary with time so you can differentiate both sides with respect to time, t, to get

[tex]\frac{dV}{dt}=36\pi \frac{dh}{dt}[/tex]

Now use the fact that [tex]\frac{dh}{dt}=3 \:{\frac{cm}{min}[/tex] to find [tex]\frac{dV}{dt}[/tex].

[tex]\frac{dV}{dt}=36\pi (3)=108\pi[/tex]

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