simplify completely 4x^3+5x^2+3x/x

Answer:

(x, y) = (- 3, 3)

Step-by-step explanation:

given the 2 equations

- x + 3y = 12 → (1)

y = 6x + 21 → (2)

Substitute y = 6x + 21 into (1)

- x + 3(6x + 21) = 12 ← distribute

- x + 18x + 63 = 12

17x + 63 = 12 ( subtract 63 from both sides )

17x = - 51 ( divide both sides by 17 )

x = - 3

Substitute  x = - 3 into (2) for y

y = (6 × - 3 ) + 21 = - 18 + 21 = 3

solution is (- 3, 3 )

Answer:

first, you add the hours driven then you divide.

2+1.4+1.25=4.65

336/4.65=72.3

Step-by-step explanation:

The problem is that Bob cannot evenly distribute his 24 fish and 18 plants across 5 tanks due to left over quantities when the numbers are divided.

The problem presented is a math problem requiring the use of division and balance. It involves Bob trying to evenly distribute his 24 fish and 18 plants across 5 tanks. An effective way is to divide the quantities of fish and plants by the number of tanks. Therefore, if there are 5 tanks, 24 fish would be divided by 5, giving 4 fish with 4 left over, and 18 plants divided by 5 gives 3 plants each with 3 left over. This indicates that an even distribution is not possible with these numbers, because there would always be a excess quantity of fish and plants beyond what can be put in the 5 tanks.

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To distribute the fish and plants without any leftover, divide the total number of fish and plants by the number of tanks.

To distribute the fish and plants without any leftover, Bob needs to divide them equally among the tanks. To find out how many fish and plants should be in each tank, we need to divide the total number of fish and plants by the number of tanks.

Number of fish in each tank = 24 fish / 5 tanks = 4 fish per tank.

Number of plants in each tank = 18 plants / 5 tanks = 3.6 plants per tank. Since we can't have a fraction of a plant, we can round it up to 4 plants per tank or distribute the leftover plant evenly among the tanks.

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Final answer:

After calculating the cost per ounce for both packages, the 10.5-ounce package, with a unit price of $0.284 per ounce, is the better deal compared to the 27.8-ounce package, which has a unit price of $0.323 per ounce.

Explanation:

To determine which package has the better unit price, you calculate the cost per ounce for each package and compare them. First, divide the total cost of each package by the number of ounces it contains.

For the 10.5-ounce package at $2.98:

$2.98 ÷ 10.5 ounces = approximately $0.284 per ounce

For the 27.8-ounce package at $8.99:

$8.99 ÷ 27.8 ounces = approximately $0.323 per ounce

Now, compare the unit prices. The 10.5-ounce package has a lower unit price of $0.284 per ounce compared to the 27.8-ounce package with a unit price of $0.323 per ounce, making the 10.5-ounce package the better deal based on unit price.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -1) and (9, -9). Substitute:

[tex]d=\sqrt{(9-7)^2+(-9-(-1))^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}\\\\=\qrt{4\cdot17}=\sqrt4\cdot\sqrt{17}=\boxed{2\sqrt{17}}[/tex]

The distance between the points (7, -1) and (9, -9) is calculated using the distance formula and simplifies to [tex]2\sqrt{17}[/tex] units.

To find the distance between two points in simplest radical form, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]. For the points (7, -1) and (9, -9), the calculation is as follows:

First, find the difference in the x-coordinates: 9 - 7 = 2.

Next, find the difference in the y-coordinates: -9 - (-1) = -8.

Now, square each difference: (2)^2 = 4 and (-8)^2 = 64.

Add these squares together: 4 + 64 = 68.

Finally, take the square root of the sum: [tex]\sqrt{68}[/tex].

This radical simplifies to [tex]\sqrt{4 * 17} = 2\sqrt{17}[/tex], which is in simplest radical form.

Therefore, the distance between the points (7, -1) and (9, -9) is [tex]2\sqrt{17}[/tex] units.

Answer:

I would combine like terms

Step-by-step explanation:

2/3x + 1/3x + =5

The first step would be to combine like terms

2/3 x + 1/3 x  = x

The graph described by the student shows a solid vertical line through the point (5, 0), with shading to the left. This corresponds to the inequality 'x less than or equal to 5'.

The student is asking about a graph of an inequality which features a solid vertical line that passes through the point (5, 0). The graph has shading to the left of this line. A vertical line in coordinate geometry represents all points where the x-coordinate is a specific value, and if the shading is to the left, it indicates that the x-values are less than or equal to that specific value of the vertical line.

Therefore, the correct inequality that matches the described graph is x less than or equal to 5 (`x ≤ 5`). The other options do not correctly represent a vertical line or the indicated shading direction.

Answer:

35q-384 = 225q-189

Step-by-step explanation:

since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189

Answer:

x = 4 1/2 or 4.5 cm

Step-by-step explanation:

We know the perimeter of the rectangle is given by the formula

P =2(l+w)

19 = 2(2.5 + (2.5+x))

Simplifying

19 = 2( 5+x)

Distribute

19 = 10 + 2x

Subtract 10 from each side

19-10 = 10-10 + 2x

9 = 2x

Divide each side by 2

9/2 = 2x/2

4.5 = x

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

Law of exponent

[tex]a^{-m} = \frac{1}{a^{m} }[/tex]

1) Applying the above rule, we have

[tex]9^{-2} = \frac{1}{9^{2} }[/tex]

= [tex]\frac{1}{9*9}[/tex]

= [tex]\frac{1}{81}[/tex]

Answer:

y = -3x-9

Step-by-step explanation:

To solve for y, we need to subtract 7 from each side

7-7 + y = -2-7 -3x

y = -3x-9

For x:

[tex]-2-3x=7+y[/tex]             add 2 to both sides

[tex]-3x=9+y[/tex]          divide both sides by (-3)

[tex]\boxed{x=-3-\dfrac{1}{3}y}[/tex]

For y:

[tex]7+y=-2-3x[/tex]      subtract 7 from both sides

[tex]\boxed{y=-9-3x}[/tex]

Answer: [tex]w=-\frac{1}{5}[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following equation given in the problem above:

[tex]5 -5w= 6[/tex]

2. Then, you need to solve for [tex]w[/tex], as you can see in the following steps:

[tex]5-5w=6\\-5w=6-5\\-5w=1\\w=-\frac{1}{5}[/tex]

3. Therefore, as you can see, the value of [tex]w[/tex] is:

[tex]w=-\frac{1}{5}[/tex]

Answer:

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Step-by-step explanation:

We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.

We need to identify the slope and y- intercept of the graph of the equation .

Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Answer:

The answer is (r + 3)(r - 3)

Step-by-step explanation:

There need to be two number that add together to get 0

and two number that multiply together to get -9

3 + -3 = 0

3 · -3 = -9

= (r + 3)(r - 3)

Answer:B

Step-by-step explanation:

The green square is the larger square, the total area for the target would be 8 x 8 = 64 square units.

The area of the smaller yellow square would be 4 x 4 = 16 square units.

The green area would be the difference between the total target area and the yellow area: 64 - 16 = 48 square units.

The probability of hitting the green area = 48 / 64 = 0.75

The answer is C.

Answer:

The equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

Step-by-step explanation

The equation of the line

y = mx + c

where m is the slope and c is the y - intercept .

As given

A line has a slope of -5 and passes through the point (2, 2).

The slope of the line is -5.

m = -5

Put in the equation of the line

y = -5x + c

Put x = 2 and y = 2

2 = -5 × 2  + c

2 = - 10  + c

2 + 10 = c

12 = c

Put the value of c in the y = -5x + c

y = -5x + 12

Therefore the equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

To find the equation of the line with slope -5 passing through (2, 2), use the point-slope form and simplify to get y = -5x + 12. Therefore, the correct answer is option D.

To find the equation of the line with a slope of -5 that passes through the point (2, 2), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.

Substituting the given values:

y - 2 = -5(x - 2)

Simplify this equation:

Therefore, the equation of the line is y = -5x + 12, so the correct answer is option D.

Answer:

c -2 -1 0 1 and 2

Step-by-step explanation:

abs (x) < 3

Absolute value equations have 2 solutions, one positive and one negative ( remember to flip the inequality when taking the negative solution).

x<3 and x>-3

-3 <x<3

The integer solutions are -2,-1,0,1-2

We do not include 3 because there is no equals sign on the inequality.

Answer:

x = 10

Step-by-step explanation:

First, we need to isolate all the x's on one side. To do this we need to move the -20 over to the other side making it a +20:

3.5x + 1/2x = 40 + 20 - 2x

Add the x's and the 40 and 20:

4x = 60 - 2x

Move the -2x over to the other side making it a +2x:

4x + 2x = 60

6x = 60

Divide both sides by 6:

x = 10

So x = 10

Answer:

10

Step-by-step explanation:

3.5(x) + -20 + 1/2(x) = 40 - 2x

3.5x - 20 + x/2 = 40 - 2x

3.5x + x/2 + 2x = 40 + 20

6x = 60

x = 60/6

    = 10

Answer:

  9/10 hours

Step-by-step explanation:

You want the total of 1/2 hours and 2/5 hours.

Addition of fractions is accomplished by converting them to values that have a common denominator.

  1/2 = 5/10

  2/5 = 4/10

Then the sum is ...

  1/2 +2/5 = (5/10) +(4/10) = (5 +4)/10 = 9/10

Manuel spent 9/10 hours on the two assignments.

__

Additional comment

Equivalently, you can convert the fractions to decimals and add them that way:

  1/2 +2/5 = 0.5 +0.4 = 0.9 . . . . . 9/10 hours

Your calculator can tell you what the sum is.

ANSWER: [tex]y=9x-23[/tex]

EXPLANATION:

We can use the slope-formula to find the slope.

[tex]\text{Slope Formula:} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{4+5}{3-2} =m\\\\\frac{9}{1} = m\\\\9=m[/tex]

Now that we have the slope, we can plug in one of the x and y values into the slope-intercept formula to find b.

[tex]\text{Slope-Intercept Formula}:y=mx+b\\\\4=9(3)+b\\\\4=27+b\\\\-23=b[/tex]

The equation of the line that passes through (3, 4) and (2, -1) is [tex]y=9x-23[/tex]

let's say that number is "x", so that is then the 100%.

if 150 is 25%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 150&25 \end{array}\implies \cfrac{x}{150}=\cfrac{100}{25}\implies \cfrac{x}{150}=4\implies x=600[/tex]

Answer:

x= 60.1 degrees

Step-by-step explanation:

The triangle forms a right angle triangle

Opposite side of angle x = 13 ft

Hypotenuse of the triangle = 15

We know the opposite side and the hypotenuse

So we use trigonometric formula sin(x)

[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]

[tex]sin(x) = \frac{13}{15}[/tex]

When we move 'sin' to the other side it becomes 'sin^-1'

[tex]x=sin^{-1}(\frac{13}{15})[/tex]

x = 60.073565

Answer:x = 60.073565

Step-by-step explanation:

Answer:

3. aₙ = -9n +7

4. d = -2.4

5. a₆ = 45

6. aₙ = 133 + 4n

Step-by-step explanation:

Question 3.

a₁ = -2; aₙ = aₙ₋₁ - 9

The explicit rule for an arithmetic sequence is

        aₙ = a₁ + d(n -1 )

         d = aₙ - aₙ₋₁

        aₙ = aₙ₋₁ - 9     Subtract aₙ₋₁ from each side

aₙ - aₙ₋₁ = -9

         d = -9

For this sequence,  

aₙ = -2 – 9(n - 1)     Remove parentheses

aₙ = -2 - 9n + 9      Combine like terms

aₙ = -9n + 7

===============

Question 4

d = aₙ - aₙ₋₁

a₂ - a₁ = 6.2 – 8.6 = -2.4

a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.

The common difference is

d = -2.4

===============

Question 5

aₙ = 8n – 3     Substitute the value of n

a₆ = 8×6 – 3

a₆ = 48 - 3

a₆ = 45

============

Question 6

a₁ = 137; d = 4

aₙ = a₁ + d(n -1 )

aₙ = 137 + 4(n -1 )

aₙ = 137 + 4n -4

aₙ = 133 + 4n

The statement is true. Amir did indeed drive from Jerusalem to the Dead Sea, which holds the distinction of being the lowest point on Earth in terms of land elevation.

True. Amir drove from Jerusalem to the Dead Sea, which is indeed the lowest place on Earth in terms of land elevation. The Dead Sea is a remarkable geographical feature located in the Jordan Rift Valley and is renowned for its extreme salinity, making it one of the saltiest bodies of water on Earth. The surface of the Dead Sea lies approximately 430 meters (1,410 feet) below sea level, and its shores border both Jordan to the east and Israel and the West Bank to the west.

Jerusalem, on the other hand, is situated on a plateau in the Judaean Mountains, and the drive from Jerusalem to the Dead Sea involves descending from higher elevations down to the low-lying area where the Dead Sea is located. This journey provides travelers with a striking transition from the elevated terrain around Jerusalem to the uniquely low and buoyant waters of the Dead Sea.

The Dead Sea's remarkable location and its high salinity levels have made it a popular destination for tourists seeking the therapeutic benefits of its mineral-rich mud and the sensation of effortlessly floating on its surface. This natural wonder's status as the lowest place on Earth is well-documented and contributes to its global renown.

For more such information on:Dead Sea

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The question probable may be:

Amir drove from Jerusalem to the lowest place on earth, the Dead Sea.   True or false.

Answer:the answer would be a i just did it but correct me if i was wrong

Step-by-step explanation:

Answer:

b. $3,000.00

Step-by-step explanation:

Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.

Grath Oil bonds are selling at 120.514

Ombor Medical Supplies bonds are selling at 90.773

Dwyn Horticulture bonds are selling at 101.180.

These values have nothing to do here as we only have to find the face value.

The face value of 1 bond is $1000 so, the face value of 3 bonds will be = [tex]1000\times3=3000[/tex] dollars.

Answer:

Take wholesale cost and multiply it by 95%, then add to the original value

another way, just multiply by 1.95

Retail cost:  1.95*($99.50) = $194.03

Final answer:

To solve 8(5x+9x+6)=160, we first combine like terms to simplify the expression within the parentheses to 14x+6, and then use the distributive property to further simplify and solve the equation. This order of operations ensures clarity and accuracy in solving the equation.

Explanation:

The question involves solving the algebraic expression 8(5x+9x+6)=160. The first step in simplifying and solving an equation like this is to combine like terms within the parentheses. Combining like terms (5x+9x) simplifies the expression inside the parentheses to 14x+6. This simplification makes the equation easier to manage and understand. The next step is to use the distributive property which allows us to multiply the number outside the parenthesis (in this case, 8) by each term inside the parenthesis individually (14x and 6). After distributing, we get 112x + 48 = 160, from which we can solve for x by isolating the variable.

The order of operations is crucial here; combining like terms before using the distributive property ensures the equation remains manageable and reduces the potential for errors. After these steps, we can subtract 48 from both sides and divide by 112 to find the value of x that satisfies the equation.

Answer:

associative property of multiplication

Step-by-step explanation:

Associative property of multiplication states that (a x b) x c = a x (b x c).

5 * (sqrt(9) *4) = (5* sqrt(9) ) *4

Answer:

$27.83

Step-by-step explanation:

26.50 x .05 = 1.325  (round up to 1.33 since the 5 is 5 or greater)  

26.50 + 1.33 = 27.83  

Amount of tax will be 1.33

Answer:

27.83

Step-by-step explanation: