(3x-2)(2x2+5x-1) what is not equivalent to the product

Answer:

Step-by-step explanation:

You want a system of equations and a graphical solution for the scenario that the weight of peaches sold (y) is 3 times the weight of apples sold (x), and the revenue from sales of apples at $3/lb and peaches at $4/lb was a total of $240.

The revenue equation can be ...

  3x +4y = 240

The relation between pounds of each fruit sold can be ...

  y = 3x

The graph is attached. The solution is (x, y) = (16, 48).

16 pounds of apples and 48 pounds of peaches were sold.

__

Additional comment

We note that the 3x in the first equation can be substituted by y using the second equation. This gives 5y=240, or y = 48. Then 3x=48, so x=16. This agrees with the graphical solution, as it should.

Answer:

x/4

Step-by-step explanation:

Answer:

It's B or C, I can't see it clearly sorry!

Step-by-step explanation:

Answer: E

Step-by-step explanation:

The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

For more such answers on range

https://brainly.com/question/30389189

#SPJ11

if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Finding the inverse of the cube of a bijective function is an important step in understanding the properties of functions. To prove that f-cube is a bijection if f is a bijection, we can use the fact that for any two real numbers x and y, if x = y, then x1/3 = y1/3. This means that if f(x) = f(y), then (f(x))3 = (f(y))3, or f-cube(x) = f-cube(y). Since f is a bijection, this means that x = y, so f-cube is also a bijection.

To find the inverse of f-cube, we can use the fact that for any real number x, x1/3 is a well-defined real number. This means that if we have f-cube(x) = y, we can take the cube root of both sides to get f(x) = y1/3. Since f is a bijection, it has an inverse function f^-1, so we can apply this inverse to both sides to get x = f^-1(y1/3). This means that the inverse of f-cube is f^-1(y1/3).

In conclusion, if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Learn more about Bijection

brainly.com/question/13012424

#SPJ11

Answer:

9% of $1500 is $15 so she gains an extra $15 for each of the 18 years

$1500 in the bank each year for 18 years is $27000 after 18 years

$15 each year as well so that’s an extra $270 in the bank

The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270

Step-by-step explanation:

Answer:

99

Step-by-step explanation:

You subtract 45 and 36 from 180

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

To know more about conversion, visit:
https://brainly.com/question/13016491
#SPJ1

Answer:

\(\frac{-1.1x^{25} }{-1.1x^{11} }\)     \(\frac{mx^{67} }{mx^{37} }\)

Step-by-step explanation:

Sine (-1.1) is the same as (-1.1) you just put them together and if the numbers are by each other you just add up the exponents. But if the question says this \(\frac{-1.1x^{2} }{-1.1x^{3} }\) than you subtract the exponents.

·\((-1.1)x^{13}X (-1.1)x^{12} = add\\\frac{-1.1x^{2} }{-1.1x^{2} } = subtract\)

Hope this helps. Have a blessed day :)

Answer:

x = 20

Step-by-step explanation:

These angles are vertical angles.

Vertical angles are congruent!! So we set them equal to one another.

2 + 3x = 62

-2           -2

3x = 60

----    ---

3       3

x = 20

Answer: x = 20

Concept:

Vertical angles: Pairs of opposite angles made by intersecting lines.

Vertical Angle Theorem: If 2 angles are vertical, then they are congruent.

If you cannot understand this, please refer to the attachment below for a graphical explanation.

Solve:

Given information

Angle 1 = (2 + 3x)°

Angle 2 = 62°

Set equation

Angle 1 = Angle 2

2 + 3x = 62

Subtract 2 on both sides

2 + 3x - 2 = 62 - 2

3x = 60

Divide 3 on both sides

3x / 3 = 60 / 3

\(\boxed{x=20}\)

Hope this helps!! :)

Please let me know if you have any questions

The time taken for the trip will be 12.7 hours.

It should be noted that time taken is calculated as:

Time = Distance / Speed

Distance = 700 miles

Speed = 55 mph

Time = 700/55

Time = 12.7 hours.

Therefore, the time taken for the trip will be 12.7 hours.

Learn more about expressions on:

brainly.com/question/22048677

#SPJ1

Answer:

Step-by-step explanation:

Before we figure out the student mistake, let us find the product of the complex numbers ourselves first.

(4+5i) (3-2i)

open the parenthesis

= 4(3)-4(2i)+3(5i)+5i(-2i)

= 12-8i+15i-10i²

Note that in complex number, i² = -1, hence the expression will become;

= 12-8i+15i-10(-1)

= 12-8i+15i+10

collect like terms by separating the real from imaginary part

= 12+10-8i+15i

= 22+7i

From the students answer i.e 12-10i, it can be concluded that;

In the multiplication of the imaginary parts, the student forgot to square the i and the student has only multiplied the real parts and the imaginary parts 4 and 3 to get 12

Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

The most appropriate comparison of the spreads between the two towns is that Town A has a smaller spread than Town B.

To understand why this statement is true, let's analyze the box plots step by step:

1. Look at the box plots for Town A and Town B. In Town A, the box extends from approximately 15°F to 30°F, while in Town B, the box extends from around 20°F to 45°F.

2. The box in a box plot represents the interquartile range (IQR), which measures the spread of the data between the first quartile (Q1) and the third quartile (Q3). In Town A, the IQR is smaller because the range between Q1 and Q3 is narrower compared to Town B.

3. Additionally, examine the whiskers of the box plots. In Town A, the whiskers span from around 0°F to 45°F, while in Town B, the whiskers extend from approximately 15°F to 60°F.

4. The whiskers indicate the range of the data excluding any outliers. Town A has a smaller range because the whiskers cover a narrower temperature range compared to Town B.

5. Based on the observations from the box plots, it is clear that the spread of temperatures in Town A is smaller than that in Town B.

Therefore, the most appropriate comparison of the spreads is that Town A has a smaller spread than Town B.

For more such questions on comparison, click on:

https://brainly.com/question/30497593

#SPJ8

The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule \(n^4+1\). The next number would then be fourth power of 7 plus 1, or 2402.

And the harder way: Denote the n-th term in this sequence by \(a_n\), and denote the given sequence by \(\{a_n\}_{n\ge1}\).

Let \(b_n\) denote the n-th term in the sequence of forward differences of \(\{a_n\}\), defined by

\(b_n=a_{n+1}-a_n\)

for n ≥ 1. That is, \(\{b_n\}\) is the sequence with

\(b_1=a_2-a_1=17-2=15\)

\(b_2=a_3-a_2=82-17=65\)

\(b_3=a_4-a_3=175\)

\(b_4=a_5-a_4=369\)

\(b_5=a_6-a_5=671\)

and so on.

Next, let \(c_n\) denote the n-th term of the differences of \(\{b_n\}\), i.e. for n ≥ 1,

\(c_n=b_{n+1}-b_n\)

so that

\(c_1=b_2-b_1=65-15=50\)

\(c_2=110\)

\(c_3=194\)

\(c_4=302\)

etc.

Again: let \(d_n\) denote the n-th difference of \(\{c_n\}\):

\(d_n=c_{n+1}-c_n\)

\(d_1=c_2-c_1=60\)

\(d_2=84\)

\(d_3=108\)

etc.

One more time: let \(e_n\) denote the n-th difference of \(\{d_n\}\):

\(e_n=d_{n+1}-d_n\)

\(e_1=d_2-d_1=24\)

\(e_2=24\)

etc.

The fact that these last differences are constant is a good sign that \(e_n=24\) for all n ≥ 1. Assuming this, we would see that \(\{d_n\}\) is an arithmetic sequence given recursively by

\(\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}\)

and we can easily find the explicit rule:

\(d_2=d_1+24\)

\(d_3=d_2+24=d_1+24\cdot2\)

\(d_4=d_3+24=d_1+24\cdot3\)

and so on, up to

\(d_n=d_1+24(n-1)\)

\(d_n=24n+36\)

Use the same strategy to find a closed form for \(\{c_n\}\), then for \(\{b_n\}\), and finally \(\{a_n\}\).

\(\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}\)

\(c_2=c_1+24\cdot1+36\)

\(c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2\)

\(c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3\)

and so on, up to

\(c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)\)

Recall the formula for the sum of consecutive integers:

\(1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2\)

\(\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)\)

\(\implies c_n=12n^2+24n+14\)

\(\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}\)

\(b_2=b_1+12\cdot1^2+24\cdot1+14\)

\(b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2\)

\(b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3\)

and so on, up to

\(b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)\)

Recall the formula for the sum of squares of consecutive integers:

\(1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6\)

\(\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)\)

\(\implies b_n=4n^3+6n^2+4n+1\)

\(\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}\)

\(a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1\)

\(a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2\)

\(a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3\)

\(\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1\)

\(\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4\)

\(\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)\)

\(\implies a_n=n^4+1\)

a.

b. The average acceleration of the car between 6.0 and 8.0 seconds is 15.0 m/s²

Average acceleration is the rate of change of velocity with time.

From the graph, we know that the gradient of each section is the acceleration of the car in each section.

For each section, we have the condition

The average acceleration a = (v₂ - v₁)/(t₂ - t₁) where

So, substituting the values of the variables into the equation, we have

a = (v₂ - v₁)/(t₂ - t₁)

a = (45.0 m/s - 15.0 m/s)/(8.0 s - 6.0 s)

a = (30.0 m/s)/(2.0 s)

a = 15.0 m/s²

So, the acceleration is 15.0 m/s²

Learn more about average acceleration here:

https://brainly.com/question/28850590

#SPJ1

Answer:

27,735

Step-by-step explanation:

43*43=1849

1849*15=27,735

Answer:

Step-by-step explanation:

15 times 43^2

15 × 43² =

15 × 1849 =

27735

Answer:

5000 aluminium cans

Step-by-step explanation:

So if the bring in ten aluminium bottles they make 1 dollar. If they bring in 50 they make 5 dollars.

If they 500 they make 50 dollars

If they bring in 5000 they make 500 dollars

Hope this helps!

The answer is:

-32

Work/explanation:

Remember the integer rule:

\(\blacktriangleright\phantom{333}\sf{a\times(-b)=-ab}\)

In other words, we multiply a positive times a negative which results in a negative product.

Therefore,

8*(-4) = -32

It will take approximately 349.1 second for the ball with diameter of 10 to deflate.

The formula for a sphere's volume is, V = (4/3)πr³ where V is the sphere's volume, r is its radius, and (pi) is a mathematical constant roughly equal to 3.14. According to this equation, a sphere's volume is equal to four-thirds of the sum of its radius's cube and the value of pi. In geometry and physics, this method is used to determine the volume of spherical objects like planets, balls, and bubbles.

The volume of a sphere is given as:

V = (4/3)πr³

Substituting the values:

V = (4/3)π(5)³ = 523.6 cubic inches

The rate is given as:

V = rt

Solving for t for the given rate we have:

t = V/r = 523.6/1.5 = 349.1 seconds

Hence, it will take approximately 349.1 seconds (or about 5.8 minutes) for the ball to deflate.

Learn more about volume of sphere here:

https://brainly.com/question/9994313

#SPJ1

Answer:

Angle 8 because it is a different measure to the other options.

Step-by-step explanation:

Congruent means the angles are the same and angle 8 is not the same as angle 7.

Answer:

Graph

\(y = -x+1\) --- Slope intercept form

\(y +x= 1\) --- Standard form

Points

\(y = 2x-2\) --- Slope intercept form

\(y -2x=-2\) --- Standard form

Step-by-step explanation:

Solving (a): The graph.

From the graph, we have:

\((x_1,y_1) = (1,0)\)

\((x_2,y_2) = (0,1)\)

First, calculate the slope

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{1 - 0}{0 - 1}\)

\(m = \frac{1 }{- 1}\)

\(m = -1\)

The slope intercept equation is:

\(y = m(x-x_1)+y_1\)

So, we have:

\(y = -1(x-1)+0\)

\(y = -1(x-1)\)

\(y = -x+1\)

In standard form:

\(y = -x+1\)

Add x to both sides

\(y +x= x-x+1\)

\(y +x= 1\)

Solving (b): The points

From the graph, we have:

\((x_1,y_1) = (0,-2)\)

\((x_2,y_2) = (3,4)\)

First, calculate the slope

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{4 - (-2)}{3 - 0}\)

\(m = \frac{6}{3}\)

\(m=2\)

The slope intercept equation is:

\(y = m(x-x_1)+y_1\)

So, we have:

\(y = 2(x-0)-2\)

\(y = 2(x)-2\)

\(y = 2x-2\)

In standard form:

\(y = 2x-2\)

Subtract 2x from both sides

\(y -2x= 2x-2x-2\)

\(y -2x=-2\)

Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

5.

1st step

Replace f(x) with y:

2nd step:

Replace every x with a y and replace every y with an x:

3rd step:

Solve for y:

4th step:

Replace y with f^-1(x)

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

The domain of f^-1(x) will be given by:

Since we can't divide by zero, so:

The range of f^-1(x) will be the domain of f(x), the domain of f(x) is given by:

Because we can't divide by zero, so:

Therefore, the range of f^-1(x) is:

Answer:

A) 30

Step-by-step explanation:

If you do 75-43 feet, you get 32 feet. Round 32 to the nearest ten, and you get 30 feet