Find the discriminant of $3x^2 + \left(3 + \frac 13\right)x + \frac 13$.

The classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent. The Option B is correct.

We have a consistent independent equation when a system of linear equations has exactly one solution. When this occurs, the graphs of the system's lines cross at exactly one point.

For our question, we can start by rearranging the first equation to isolate y:

[tex]4x + y = 4\\y = -4x + 4[/tex]

We can see that the second equation is already in the form y = mx + b, where m is the slope and b is the y-intercept. So we can identify that the slope of the second equation is -4 and the y-intercept is 4.

Now we can compare the slopes and y-intercepts of the two equations to determine the classification of the system of equations:

In this case, we can see that the slopes of the two equations are different (-4 and 0) and the y-intercepts are the same (4). Therefore, the system is consistent and there is a unique solution. So the classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent

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Answer:

need brainly point

Step-by-step explanation:

The system of equations for this problem is:
Basic: 1x + 1.5y + z = 75.7
Homeowner: 4x + 1.7y + 1.6z = 57.9
Pro: 3x + 1.5y + 1.4z = 46.6

To solve this problem using inverse matrices, we first need to create the matrices of coefficients and constants:
Coefficient Matrix:
[[1, 1.5, 1],
[4, 1.7, 1.6],
[3, 1.5, 1.4]]

Constant Matrix:
[[75.7],
[57.9],
[46.6]]

Next, we can use inverse matrices to find the solution:
Inverse of Coefficient Matrix =
[[-9.38, 7.81, 3.2],
[4.69, -3.81, -1.6],
[3.46, -2.81, -0.8]]

Solution =
[[-9.38*75.7 + 7.81*57.9 + 3.2*46.6],
[4.69*75.7 - 3.81*57.9 - 1.6*46.6],
[3.46*75.7 - 2.81*57.9 - 0.8*46.6]]

Therefore, the manufacturer can produce
Basic sets,
Homeowner sets and
Pro sets per day

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Based on the information, we can infer that the graph would be as shown in the attached image.

To graph the equations we must identify the values of the coordinates of each of the equations. In this case it would be:

Equation 1:

Equation 2:

According to the above, the lines would look as shown in the graph. In the case of the first equation, it would be represented by the red line and the second equation would be represented by the blue line.

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The car's value will decrease at rate of 1/5.

Rate refers to the ratio between two quantities with different units. For example, if you travel 100 miles in 2 hours, your rate of speed would be 50 miles per hour (mph).

From the graph, we have the following:

1: At mileage (x) = 20,000 miles, value of car (y) = $12000

2: At mileage (x) = 40,000 miles, value of car (y) = $8000

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

Rate = (8000 - 12000)/(40000 - 20000)

Rate = -1/5

Thus, the car's value will decrease at rate of 1/5.

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Complete Question

Check attached image

Jacob needs 290.92 ft² of carpet in total to cover both the living room and the dining room.

To find out how much carpet Jacob needs to cover his living room, we can multiply the length and width of the room:

15 ft x 12 1/3 ft = 15 ft x (37/3) ft = 555/3 ft²

To simplify this fraction, we can divide both the numerator and denominator by 3:

555/3 ft² = 185 ft²

So the living room requires 185 square feet of carpet.

To find out how much carpet Jacob needs to cover his dining room, we can multiply the length and width of that room:

10 1/4 ft x 10 1/3 ft = (41/4) ft x (31/3) ft = 1271/12 ft²

To simplify this fraction, we can divide both the numerator and denominator by 1:

1271/12 ft² = 105.92 ft² (rounded to two decimal places)

So the dining room requires 105.92 square feet of carpet.

To find out how much carpet Jacob needs in total, we can add the amount of carpet required for each room:

185 ft² + 105.92 ft² = 290.92 ft²

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The density of the apple juice is approximately 1094 kg/m³.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

To calculate the density of the apple juice in kilograms per cubic metre (kg/m³), we need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) and the mass from grams to kilograms.

1 cm³ = (1/100)^3 m³ = 10^-6 m³ (conversion factor from cm³ to m³)

1 g = (1/1000) kg (conversion factor from g to kg)

So, the volume of the apple juice in cubic meters is:

320 cm³ × (10^-6 m³/cm³) = 0.00032 m³

And the mass of the apple juice in kilograms is:

350 g × (1/1000) kg/g = 0.35 kg

Now, we can calculate the density using the above formula:

p = m / v

p = 0.35 kg / 0.00032 m³

p = 1093.75 kg/m³

p = 1094 kg/m³

Therefore, the density is 1094 kg/m³.

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a. The owners' equity increased from $1,567 in 2014 to $3,122 in 2015.

b. The change in net working capital for 2015 is $168.

c. The amount of fixed assets did Weston Enterprises sold is $1630

d. Weston Enterprises must have paid off $2,253 in long-term debt during the year

Now, let's move on to the questions.

a. To find the owners' equity for 2014 and 2015, we need to subtract the total liabilities from the total assets. For 2014, the calculation would be,

Owners' equity 2014 = Total assets 2014 - Total liabilities 2014

Owners' equity 2014 = (Current assets 2014 + Net fixed assets 2014) - (Current liabilities 2014 + Long-term debt 2014)

Owners' equity 2014 = (964 + 4,384) - (401 + 2,380)

Owners' equity 2014 = $1,567

For 2015, the calculation would be:

Owners' equity 2015 = Total assets 2015 - Total liabilities 2015

Owners' equity 2015 = (Current assets 2015 + Net fixed assets 2015) - (Current liabilities 2015 + Long-term debt 2015)

Owners' equity 2015 = (1,176 + 5,104) - (445 + 2,713)

Owners' equity 2015 = $3,122

b. The change in net working capital for 2015 can be calculated by subtracting the net working capital for 2014 from the net working capital for 2015. Net working capital is the difference between current assets and current liabilities.

Net working capital 2014 = Current assets 2014 - Current liabilities 2014

Net working capital 2014 = 964 - 401

Net working capital 2014 = $563

Net working capital 2015 = Current assets 2015 - Current liabilities 2015

Net working capital 2015 = 1,176 - 445

Net working capital 2015 = $731

Change in net working capital = Net working capital 2015 - Net working capital 2014

Change in net working capital = 731 - 563

Change in net working capital = $168

c. To find out how much in fixed assets Weston Enterprises sold, we need to use the equation for the cash flow from assets,

Cash flow from assets = Cash flow to creditors + Cash flow to owners

Cash flow from assets = (Interest paid - Net new long-term debt) x (1 - Tax rate) + (Depreciation x Tax rate)

Cash flow from assets = (328 - (2,713 - 2,380)) x (1 - 0.4) + (1,190 x 0.4)

Cash flow from assets = (-$57) + $476

Cash flow from assets = $419

Net increase in fixed assets = Net fixed assets 2015 - Net fixed assets 2014

Net increase in fixed assets = 5,104 - 4,384

Net increase in fixed assets = $720

Amount of fixed assets sold = Net increase in fixed assets - New fixed assets purchased

Amount of fixed assets sold =  $2,350 - $720

Amount of fixed assets sold = $1,630

d. To calculate the amount of long-term debt paid off during the year, we need to use the equation for the cash flow to creditors,

Cash flow to creditors = Interest paid - Net new long-term debt

Cash flow to creditors = $328 - ($455 - $2,380)

Cash flow to creditors = $2,253

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Given that two of the angles in this triangle are equal and have a measure of 78 degrees and sides 4x + 23, 10x-1 the solution x = -1.15 is a valid solution.

What is the inequality equation?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

In a triangle, the sum of the measures of the angles is always 180 degrees. Since we are given that two of the angles in this triangle are equal and have a measure of 78 degrees each, the third angle must have a measure of:

180 - 78 - 78 = 24 degrees

Now we can use the Law of Cosines to set up an equation to solve for x. The Law of Cosines states that:

c² = a² + b² - 2abcos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

We can choose any of the sides to be the side opposite the 24-degree angle, but let's use side 2, which has a length of 10x - 1. Then we have:

(10x - 1)² = (4x + 23)² + (side 3)² - 2(side 3)(4x + 23)cos(78)

Simplifying and solving for side 3, we get:

(side 3)² = (10x - 1)² - (4x + 23)² + 2(10x - 1)(4x + 23)cos(78)

(side 3)² = 36x² + 360x + 840

Taking the square root of both sides, we get:

side 3 = √(36x² + 360x + 840)

Now we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have:

side 1 + side 2 > side 3

4x + 23 + 10x - 1 > √(36x² + 360x + 840)

14x + 22 > √(36x² + 360x + 840)

Squaring both sides, we get:

196x² + 616x + 484 > 36x² + 360x + 840

Simplifying and rearranging, we get:

160x² + 256x - 356 < 0

We can solve this inequality using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 160, b = 256, and c = -356.

Plugging in these values, we get:

x = (-256 ± √(256² - 4(160)(-356))) / 2(160)

x = (-256 ± √(124160)) / 320

x = (-256 ± 352) / 320

x = 0.30 or x = -1.15

However, we need to check that these values satisfy the inequality we found earlier:

14x + 22 > √(36x² + 360x + 840)

For x = 0.30, we get:

14(0.30) + 22 > √(36(0.30)² + 360(0.30) + 840)

25.2 > 25.2

This is not true, so x = 0.30 does not work.

For x = -1.15, we get:

14(-1.15) + 22 > √(36(-1.15)² + 360(-1.15) + 840)

3.3 > 3.3

This is true, so x = -1.15 is a valid solution.

Therefore, the solution x = -1.15 is a valid solution.

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The total amount that must be repaid is $139,076.12.

Annual simple interest is a type of interest that is calculated on the principal amount of a loan or investment for a one-year period. Simple interest is a fixed percentage of the principal amount, which is added to the principal at regular intervals. The interest is calculated only on the original principal amount and does not include any interest earned on the interest itself.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on the interest earned on that principal amount over time. In other words, compound interest is interest that is added to the principal amount, and then interest is calculated on the new total amount (principal + interest). This process is repeated at regular intervals, such as monthly or annually.

In the given question, The total amount that must be repaid can be found using the simple interest formula:

I = Prt

Where:

P = principal amount borrowed = $87,495

r = annual interest rate = 8.355%

t = time period in years = 7

So, substituting the values we get:

I = 87,495 * 0.08355 * 7 = 51,581.12

Therefore, the total amount that must be repaid is:

87,495 + 51,581.12 = 139,076.12

Rounding to the nearest cent, the answer is $139,076.12.

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Answer:

27

Step-by-step explanation:

9+15=24

72/24=3   so 1=3 and there are 9 cargo cars so 9*3=27

you can also check by doing 3*15=45 and 45+27=72 so this is correct

Answer:

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

Find the area using formula:

Substitute values into formula to get:

Since each pig gets 2*5³ m² of land, by dividing the area by this number, Daniel can put:

A. x+x+11 is the expression can be best simplified for equation 2x+11

A statement that establishes the equivalence of two expressions is known as an equation in mathematics. It has two sides containing expressions on each, each separated by the equals symbol (=).

For example, the equation x + 2 = 5 asserts that the expression on the left side, x + 2, is equal to the expression on the right side, 5. This equation can be solved for the variable x, by subtracting 2 from both sides, to obtain x = 3, which is the value that satisfies the equation.

Given equation 2x+11

2x can be written as x+ x

So, expression can be written as

x+x+11

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The value of x in the triangle is 2√3

Right triangles are triangles with one angle measuring 90 degrees.

From the question, we have the following parameters that can be used in our computation:

The triangle

From the triangle, we have the following equation

x/2 = 6/x

Cross multiiply the equation

So, we have the following representation

x^2 = 12

Take the square roots of both sides

So, the equation becomes

x = 2√3

Hence, the value of x is 2√3

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Answer:

i dont

Step-by-step explanation:

never mind sorry for bothering you! :(

The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.

In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.

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Full question:

Which word BEST describes 9(2x+6y)

A Constant

B. Equation

c. Expression

D. Inequality

Answer:

1.65

Step-by-step explanation:

The first number is 1.95, to find the rest we must keep subtracting 0.15 from the previous.

1.95-0.15 = 1.8 (second number)

1.8-0.15 = 1.65 (third number)

Above, we find our answer with the 3rd number.

Niesa sent apprοximately 423 texts last mοnth.

In mathematics, an equatiοn is a fοrmula that expresses the equality οf twο expressiοns, by cοnnecting them with the equals sign =.

The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French an équatiοn is defined as cοntaining οne οr mοre variables, while in English, any well-fοrmed fοrmula cοnsisting οf twο expressiοns related with an equals sign is an equatiοn.

Let T be the number οf texts that Niesa sent last mοnth.

We can set up the equatiοn:

Tοtal cοst = fixed fee + (cοst per text x number οf texts)

$53.84 = $20 + ($0.08 x T)

Sοlving fοr T, we can subtract $20 frοm bοth sides:

$33.84 = $0.08 x T

Then, we can divide bοth sides by $0.08:

T = $33.84 / $0.08

T ≈ 423

Therefοre, Niesa sent apprοximately 423 texts last mοnth.

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Answer:

  x = 30

Step-by-step explanation:

You want the measure of the acute angle where a tangent meets a chord that intercepts an arc of 300°.

An angle inscribed in a circle has half the measure of the arc it intercepts.

If one leg of that inscribed angle degenerates in length to zero, then the "inscribed" angle becomes the angle between the remaining chord and the tangent to one end of that chord.

In other words, the measure of the angle marked x° is half the measure of the arc it intercepts.

  x° = 1/2(360° -300°) = 1/2(60°)

  x° = 30°

The value of the variable x is 30.

In response to the query, we can state that Therefore, the area of the base of the triangular pyramid is 21 square inches.

A pyramid is a polygon in mathematics, formed by connecting points referred to as bases and polygonal vertices. For each hace and vertex, a triangle called a face is formed. a cone with a polygonal form. A pyramid with a floor and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The vertex, the intersection of a pyramid's flat tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that connect to the top are formed by the edges of the base.

volume of a triangular pyramid

V = (1/3) * Base Area * Height

65 = (1/3) * Base Area * 9.75

Area = 65 / (1/3) / 9.75

Area = 21

Therefore, the area of the base of the triangular pyramid is 21 square inches.

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The work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.

Given that an object is moved 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees.To find the work done in moving an object, we know thatWork done = Force * Distance * cos(θ)Where θ is the angle between the force applied and the displacement of the object.Here, force applied = 70 poundsDistance = 30 feetAnd θ = 30 degreesWe know that the force is applied at an angle of 30 degrees to the horizontal, thus the horizontal component of the force is given by:Horizontal component of force = Force × cos (θ)So, the horizontal component of the force applied is:Horizontal component of force = 70 cos 30°= 60.62 pounds (approx)Therefore, the work done in moving the object 30 feet horizontally is:Work done = force × distance × cos (θ)= 60.62 × 30 × cos 0.5= 60.62 × 30 × 0.87= $1582.07 \text{ ft-lbs}$Therefore, the work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.

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Answer:7.8

Step-by-step explanation:

[tex]\sqrt{6^2+5^2}[/tex]

evaluate the equation / expression

7.81025

Round 7.81025 to the required place

7.8

Answer:

7.8m

Step-by-step explanation:

To find:-

Answer:-

From the given data i made a figure to represent the given situation. To find the distance between the opposite corners we would have to use Pythagoras theorem, .

The distance between the corners represents the hypotenuse of the right angled triangle and another two sides are represented by 5m and 6m .

According to Pythagoras theorem,

[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]

Here a is 5m and b is 6cm .

[tex]\rm\implies (5m)^3+(6m)^2 = h^2 \\[/tex]

[tex]\rm\implies 25m^2+36m^2=h^2\\[/tex]

[tex]\rm\implies 61m^2=h^2\\[/tex]

[tex]\rm\implies h =\sqrt{61m^2} \\[/tex]

[tex]\rm\implies \red{ h = 7.8 \ m } \\[/tex]

Hence the distance between the opposite corners is 7.8 m

Answer: 17

Step-by-step explanation:

To find much each pass earns per day is to divide the two numbers. $207 divided by 3 is 69 and $364 divided by 7 is 52. Then you subtract 69 and 52 which is 17!

Yes, a regular polygon's diagonals are all congruent.

In geometry, a shape's diagonals are its building blocks. In mathematics, a diagonal is a line that connects two solids or polygons whose vertices are not next to one another's edges. In general, a diagonal connects the vertices of a form via sloping or slanting lines. Shapes with lateral sides, edges, and corners are referred to as "diagonals" in this context. Diagonals can be found in curved objects like circles, spheres, cones, and so on.

The diagonals of a square are the segments of lines joining its opposite vertices. A square is made up of two diagonals. The two diagonals of the square are parallel to one another. The diagonals of a square divide one another in half. Each diagonal divides the square into two identical, isosceles right triangles.

Yes all of the diagonal of a regular polygon is congruent , because all sides of regular shape are congurent.

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This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound

So equation becomes C = 0.70x

We can use proportional reasoning to set up an equation to represent the cost, C, of x pounds of bananas.

We know that 20 pounds of bananas cost 14, so the cost per pound can be found by dividing the total cost by the total weight:

Cost per pound = Total cost / Total weight

Cost per pound = 14 / 20 pounds

Cost per pound = 0.70 per pound

Now, we can use this cost per pound to set up an equation:

C = cost of x pounds of bananas

x = number of pounds of bananas

Cost per pound = 0.70

So, we can write the equation as:

C = 0.70x

This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound, 0.70.

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Answer: 34

Step-by-step explanation:

based on the given conditions , formulate

[tex]\sqrt{16^2+30^2}[/tex]

x= [tex]\sqrt{(16)^2f(30)^2}[/tex]

x= [tex]\sqrt{256+900}[/tex]

x= [tex]\sqrt{11 56}[/tex]

x=  34

Answer: x-3

Step-by-step explanation: if Martin's age is unknown and we have to use x for it, you could only plug in x-3 to figure out Jennifer's age. And if we have to write an expression for Connor's age it would be x*2

martin = x years

jennifer = x - 3

Answer:

y = 4x + -8

hope this helps <3

Given the above parallelogram,

1) ∠ABC = 90°

2) ∠BCD = 90°
3) ∠CDA = 90°
4)  ∠DAB = 90°

To find the value of the angles, we need to first find x. Given that ∠ABC  = (x+35)° on the basis of opposite angles in a parallelogram, and

∠CDA = (180-(3x-75)°

since ∠ABC and ∠CDA  are opposite angles.

We can state that
(180-(3x-75)° = (x+35)°  since opposite sides of a parallelogram are equal.
Simplifying the above, we can find x:

180 - (3x - 75) = 180 - 3x + 75 = 255 - 3x

Now we can substitute this expression into the original equation:

255 - 3x = x + 35

To solve for x, we want to isolate the variable on one side of the equation. Let's start by adding 3x to both sides:

255 = 4x + 35

Next, we can subtract 35 from both sides:

220 = 4x

Finally, we can divide both sides by 4 to get the value of x:

x = 55

Therefore, the solution to the equation is x = 55°.

Since x = 55°

∠ABC  = (x+35)°

∠ABC = 55 + 35

∠ABC = 90°


Also, since:
∠CDA = (180-(3x-75)°)
∠CDA = 180- (165-75)

∠CDA = 90°

Since ∠DAB = (3x-75)° on the basis of alternate angles,
∠DAB = (3(55) -75)°

∠DAB  = 165 -75

∠DAB  = 90°


Since  ∠DAB is opposite ∠BCD and Opposite angles of a parallelogram are equal, thus, ∠BCD is also 90°

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Answer:

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

8 1/2 - 2 = 8 + 1/2 - 2 = 6 1/2

Next, we need to evaluate the exponent:

2^2 = 2 x 2 = 4

Now, we can substitute the simplified values into the expression:

7 1/4 x 4 + (6 1/2) ÷ 3

Next, we need to evaluate the multiplication and division from left to right:

7 1/4 x 4 = 29 + (6 1/2) ÷ 3

6 1/2 ÷ 3 = 2 1/6

Substituting the simplified value:

29 + 2 1/6

Next, we need to add the two values:

29 + 2 1/6 = 31 1/6

Therefore, the final answer is 31 1/6.