9 + a - 5b - 2 combine The like terms to create an equivalent expression

Answer:

29 lbs of potatoes

Step-by-step explanation:

$45 divided by 5 lbs = 9 ($9 per lb)

$261 divided by 9 = 29

Answer:

50.49%

Step-by-step explanation:

What is the percentage of 206 out of 408?

50.49% is the percentage of 206 out of 408. See below for instructions on how to convert 206/408 to percentage manually.

How to convert 206/408 to Percent

Percent Formula = X/Y *100, where

X = 206

Y = 408

Percent = 206/408*100 = 50.49%

The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The computation shows that the examples of values that will give the exact value of 45 will be:

It should be noted the information is incomplete as the options aren't given and not properly written.

In this case, the examples will be given:

An example of value that will give 45 will be:

= ✓25 × ✓81

= 5 × 9

= 45

The other examples will be 6 × 9 which will give 45 and ✓9 × 15 which will be 45.

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Alexander is utilizing a scale of 1 inch : 300 feet for his map.

The Alexander's triangle has a height of 4 inches in inches.

When comparing the initial dimensions as used by alexander, the scale of the map may be determined.

The scale is 1 inch: 300 feet since he used 10 inches to symbolize 3000 feet, this is gotten by diving both sides by 10

Using the scale factor 1 inch: 300 feet, the height of 1200 feet would be.

300 feet per inch, then ? inch is 1200 feet

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

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

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

slope = 5/-4

Therefore, the slope between the two points is -5/4.

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer:

(4x-5)(4x+5)

Step-by-step explanation:

16x^2 - 25

Rewriting

(4x)^2 - 5^2

We recognize that this is the difference of squares

a^2 - b^2 = (a-b) (a+b)

(4x)^2 - 5^2 = (4x-5)(4x+5)

(4x-5)(4x+5)

16x^2 - 25

Rewriting

(4x)^2 - 5^2

We recognize that this is the difference of squares

a^2 - b^2 = (a-b) (a+b)

(4x)^2 - 5^2 = (4x-5)(4x+5) is the ansswer to the question

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, \(W(t)=7e^{-3t}\). The general solution of the given system is written as \(x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right]\).

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is \(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x\).

Let's differentiate x₁ concerning t, and we get,

\(\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}\)

From this, we can write,

\(x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1\)

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

\(\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}\)

From this, we can write,

\(x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2\)

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

\(\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}\)

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

\(\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}\)

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

\(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right]\)

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Answer:

240 teachers

Step-by-step explanation:

Let u be 1 unit.

1u+12u=260

13u=260

u=260÷13

=20

No. of teachers=12u=20×12

=240

Let teacher be x

\(\\ \sf\longmapsto x+12x=260\)

\(\\ \sf\longmapsto 13x=260\)

\(\\ \sf\longmapsto x=\dfrac{260}{13}\)

\(\\ \sf\longmapsto x=20\)

The equation of the tangent at (2,7) is y = 4x - 1.y = x^2 + 3; t = 2

Given: y = x^2 + 3 and t = 2

We need to find the equation of the tangent at (2,7).

First, we find the slope of the tangent line by taking the derivative of the function:

y' = 2x

At x = 2, the slope is 2*2 = 4.

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

y - 7 = 4(x - 2)

Simplifying:

y = 4x - 1

Therefore, the equation of the tangent at (2,7) is y = 4x - 1.

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Answer: False

Step-by-step explanation:

\(\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}\)

The domain is all x-values.

The range is all y-values.

Domain: 3, 5, -3, 2, 1

Range: 4, 7, 8, 0, 3

Best of Luck!

Step-by-step explanation:

what is the ability that the children will have green eyes collar

Answer:(2I3O-9247)

Step-by-step explanation:

The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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Answer:

1.60x=32.00

Step-by-step explanation:

Since you do not how much gallons of gas he bought you would use the variable x.

Answer:

1.60x=32

Step-by-step explanation:

Answer:

(1,5)

Step-by-step explanation:

Hope this is right.

Answer:

It's (1,0)

Step-by-step explanation:

I got it right on the quiz

For some reason, the value of "w" is not supplemented into the equation, which is weird, but whatever. I will answer the problem for you.

The answer you are looking for is -5.

Solution/Explanation:

Writing out the expression first

-7/3x+y²

Substituting the given values of the variables, only "x" and "y"

-7/3(6)+(-3)²

Simplifying

(-7/3)(6)=-14

(-3)²=9

So, we will come up with -14+9.

This simplifies to -5.

So, therefore, the final answer to this problem is -5.

Hope this helped answer your question for you. Good day to you.

9514 1404 393

Answer:

  -5

Step-by-step explanation:

Put the values of the variables where the variables are and do the arithmetic.

  \(-\dfrac{7}{3}x +y^2=-\dfrac{7}{3}\times6+(-3)^2=-\dfrac{7\cdot6}{3}+9\\\\=-14+9=\boxed{-5}\)

Answer:

6 acres

6/7 lb left

Step-by-step explanation:

Each 7/8 of a lb is good for 1 acre.

He has 6 lb.

The first step is to see how many amounts of 7/8 lb are in 6 lb.

This is a division problem.

6 / (7/8) = 6/1 * 8/7 = 48/7 = 6 6/7

6 lb is 6 6/7 portions of 7/8 lb.

Since each 7/8 lb is good for 1 acre, he has enough for 6 6/7 acres.

He can plant 6 whole acres.

The remaining seed is 6/7 lb.

Answer: Yes, it is congruent.

Rt is same length as Tu

angle rst is equal to angle tvu

therefore the angle where they both meet would have to be the same aswell, so it is congruent

Step-by-step explanation:

Answe is attached in the above image.

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

Answer:

\(V=763.407\) yd^3

Step-by-step explanation:

Formula for volume of right circular cylinder.

\(V=\pi r^{2}*6\)

\(r=\frac{d}{2}\)

We are given the diameter (d) and the height (h).

First solve for r.

\(r=\frac{18}{2}\)

\(r=9\)

Now we have everything we need to find the volume. Plug in r into the volume formula.

\(V=\pi *9^{2} *3\)

\(V=763.407\) yd^3

Answer:

  5 months

Step-by-step explanation:

We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...

  x^6 -25x^4 +199x^2 -4975 = 0

This can be factored in groups as ...

  x^4(x^2 -25) + 199(x^2 -25) = 0

  (x^4 +199)(x^2 -25) = 0

This has 4 complex solutions and 2 real solutions.

  x^2 = 25

  x = ±5

The duration required for capacity to reach 4975 units is 5 months.

Answer:

The height would be 16 hope this helps:)!!!

The area of a parallelogram is the length x the height.

You are given the area and the length.

To find the height divide the area by the length.

Height = 240/15 = 16 inches.

Answer:

4.3 *10^3

Step-by-step explanation:

Answer:

8*5=40

160/40=4

to recheck

V= LxWxH

V=8*5*4

V=160

Step-by-step explanation:

GOOD LUCK

Answer:

Step-by-step explanation:

78 cm

Answer:

33.8

Step-by-step explanation: