Consider the difference below.

x-3/x^2-x-5 - 5/8x
Place the steps require to simplify the given difference of two expressions into one, simplified rational expression in the correct order.

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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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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Answer:

Step-by-step explanation:

The sine model is y=10 sin(1/30 t) + 30.  The 30 represents default distance from the ground, and the ten is required to represent the length of the blades.  Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.

Answer: The difference between 125 million dollars and 312.5 million dollars is, 187.5 Million Dollars.

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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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 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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The third side of the given Pythagorean triple-right-angled triangle is 32.02 units.

As per the formula pertaining to the Pythagorean triple-right-angled triangle, we have the:

h = √{(a)^2+(b)^2} .........(i),

Where, (h) = Third side of a Pythagorean triple-right-angled triangle,

(a) = First side of a Pythagorean triple-right-angled triangle = 20 units

(b) = Second side of a Pythagorean triple-right-angled triangle = 25 units

Substituting the values in equation (i), we get:

h = √{(20)^2+(25)^2} units,

or, h = √(1025) units,

or, h = 32.015 units = rounded off to 32.02 units.

Hence the third side of the given Pythagorean triple-right-angled triangle is 32.02 units.

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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:

The final answer is 18-2 = which is 16

Step-by-step explanation:

x =3

y =2

6(3) -2

Then do 18-2

You have to multiply 6 and 3, after that, subtract by 2

Just substitute your value in!

Answer:

16

Step-by-step explanation:

6x - y =

6 * 3 - 2 =

18 - 2 =

16

The resultant force on the box, along with it's direction, is given as follows:

5N Down.

The resultant force on the box is obtained as the vector sum of all the forces in the box.

The forces are given as follows:

The horizontal forces are the same force in opposite directions, hence the horizontal forces are of zero.

The sum of the vertical forces is given as follows:

5 - 10 = -5N.

As the sum is negative, the direction is in the down direction, hence the resultant force is of -5N down.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(3\times10^6) + (5\times10^7)}\\\mathsf{= (3\times10\times10\times10\times 10\times10\times10) + (5\times 10\times10\times10 \times 10\times10\times10 \times 10)}\\\mathsf{= (3\times 100\times100\times100) + (5\times100\times100\times100\times10)}\\\mathsf{= (3\times10,000\times100) + (5\times10,000\times1,000)}\\\mathsf{= (3\times1,000,000) + (5\times10,000,000)}\\\mathsf{= (3,000,00) + (50,000,000)}\\\mathsf{= 3,000,000 + 50,000,000}\\\mathsf{= 53,000,000}\\\mathsf{= 5.3\times10^7}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{5.3\times10^7}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

need brainly point

Step-by-step explanation:

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

The fraction of the material that each strip represents is 1/12 of a yard.

Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.

Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.

Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of 4 is 1/4, so we can rewrite the expression as:

1/3 ÷ 4 = 1/3 × 1/4

Now we can multiply the fractions:

1/3 × 1/4 = 1/12

Therefore, each strip represents 1/12 of the whole yard of material.

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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.

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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Answer:

i dont

Step-by-step explanation:

never mind sorry for bothering you! :(

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: 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

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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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

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

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.

A repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. 32 subjects participated in this study.

A matched-subjects experiment produced a t statistic with a df of 17.

34 subjects participated in this study.

Both a repeated-measures experiment and a matched-subjects experiment share the following characteristics when used to compare two treatment conditions:

1. They both use the same t statistic.
2. The researcher computes difference scores to compute a t statistic.
3. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.

For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31.

The number of subjects that participated in this study is 32 because the degrees of freedom (df) for a repeated measures experiment is calculated as (number of subjects - 1),

so 31 + 1 = 32.

A matched-subjects experiment produced a t statistic with a df of 17.

In this case,

the number of subjects that participated in the study is 34 because the degrees of freedom (df) for a matched-subjects experiment is calculated as (number of pairs - 1),

since there are two subjects in each pair, 17 + 1 = 18 pairs, which means 18 * 2 = 34 subjects.

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Answer:

[tex]\mbox{\large y = -\dfrac{3}{5}x - 4}[/tex]

Step-by-step explanation:

The given equation is
[tex]\mbox{\large 6x + 10y = - 40}[/tex]

The slope-intercept form of the equation of a line is
[tex]y = mx +b[/tex]

where
m = slope

b = y-intercept

Subtract 4x from both sides of [tex]\mbox{\large 6x + 10y = - 40}[/tex]

[tex]6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4[/tex]

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

The differential equation with initial conditions describing the motion is F = -k * (s(t) + 5) - 6g and the displacement of the mass from its equilibrium position as a function of time s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)

The differential equation for the motion of the mass is given by Newton's Second Law, F = ma:

F = -k * (s(t) + 5) - 6g

where k is the spring constant, s(t) is the displacement from the equilibrium position, and g is the acceleration due to gravity. The initial conditions are s(0) = 3 and s'(0) = 0, since the spring is initially stretched an additional 3 cm and released from rest.

We can rearrange the equation to get:

s''(t) + (k/6) * s(t) = -5k/6 - g

This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:

s(t) = C1 * e^(r1*t) + C2 * e^(r2*t)

where r1 and r2 are the roots of the characteristic equation:

r^2 + (k/6) * r = -5k/6 - g

Using the quadratic formula, we get:

r1,2 = -(k/12) ± √((k/12)^2 + 5k/6 + g)

We can find the values of C1 and C2 by applying the initial conditions:

s(0) = C1 + C2 = 3

s'(0) = C1 * r1 + C2 * r2 = 0

Solving for C1 and C2, we get:

C1 = (3 * r2) / (r2 - r1)

C2 = (3 * r1) / (r1 - r2)

Substituting back into the general solution, we get:

s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)

This is the displacement of the mass from its equilibrium position as a function of time.

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[  1  -0.0004    -0.00202    |  0.0404 ] [  0   1         -0.00020828 |  6] this is the Gauss Jordan elimination method step by step of the given linear equation.

The Gauss Jordan elimination method is a systematic way of solving a system of linear equations by performing elementary row operations on an augmented matrix. The augmented matrix is formed by combining the coefficients and constants of the linear equations.

The given system of linear equations can be written in matrix form as:

[  99  -0.04  -0.2  |  4  ]

[ -0.1  0.97   0    |  6  ]

[ -0.2  -0.01  0.96 |  3  ]

The goal of the Gauss Jordan elimination method is to transform the augmented matrix into reduced row echelon form, which is a unique form that represents the solution of the system of linear equations.

The following steps outline the Gauss Jordan elimination method to solve the given system of linear equations:

Step 1: Begin with the first column and eliminate the coefficients below the first row by using row operations.

Divide the first row by 99 to make the leading coefficient equal to 1:

[  1   -0.0004  -0.00202  |  0.0404  ]

[ -0.1  0.97     0        |  6       ]

[ -0.2 -0.01     0.96     |  3       ]

Add 0.1 times the first row to the second row:

[  1   -0.0004  -0.00202  |  0.0404 ]

[  0   0.9704  -0.000202 |  6.00404]

[ -0.2 -0.01     0.96     |  3      ]

Add 0.2 times the first row to the third row:

[  1   -0.0004  -0.00202  |  0.0404 ]

[  0   0.9704  -0.000202 |  6.00404]

[  0   -0.00018  0.960396 |  3.00808]

Step 2: Continue with the second column and eliminate the coefficients below the second row by using row operations.

Divide the second row by 0.9704 to make the leading coefficient equal to 1:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6.18377]

[  0  -0.00018    0.960396   |  3.00808]

Add 0.00018 times the second row to the third row:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6.18377]

[  0   0.0000324  0.96052174|  3.01998]

Step 3: Continue with the third column and eliminate the coefficients above the third row by using row operations.

Divide the third row by 0.96052174 to make the leading coefficient equal to 1:

[  1  -0.0004    -0.00202    |  0.0404 ]

[  0   1         -0.00020828 |  6]

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