Which table of ordered pairs represents a proportional relationship?
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 3, negative 4, negative 5. Column 2 is labeled y with entries 3, 2, 1.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 1, negative 3, negative 5. Column 2 is labeled y with entries 1, 3, 5.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 2, negative 4, negative 6. Column 2 is labeled y with entries negative 5, negative 7, negative 9.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 2, negative 3, negative 4. Column 2 is labeled y with entries 0, negative 1, negative 2.

In the fractions prompts given, the correct output are:

A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.

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Answer: 117.8

Step-by-step explanation:

To find the surface area of a rectangular pyramid, we need to find the area of each face and add them up.

First, we can find the area of the rectangular base:

Area of base = length x width = 6 in x 5 in = 30 in²

Next, we can find the area of each of the four triangular faces. For the two larger triangular faces:

Area of each larger face = 0.5 x base x height = 0.5 x 6 in x 7.8 in = 23.4 in²

And for the two smaller triangular faces:

Area of each smaller face = 0.5 x base x height = 0.5 x 5 in x 8 in = 20 in²

Now we can add up the areas of all the faces to find the total surface area of the pyramid:

Surface area = Area of base + 2 x Area of larger face + 2 x Area of smaller face

Surface area = 30 in² + 2 x 23.4 in² + 2 x 20 in²

Surface area = 117.8 in²

Therefore, the surface area of the rectangular pyramid is 117.8 square inches.

Answer:

116.8 in^2.

Step-by-step explanation:

To find the surface area of the rectangular pyramid, we need to find the areas of all the faces and add them together.

The area of the rectangular base is:

Area of base = length x width = 6 in x 5 in = 30 in^2

The area of each of the two large triangular faces is:

Area of triangle = 1/2 x base x height = 1/2 x 6 in x 7.8 in = 23.4 in^2

So, the total area of the two large triangular faces is:

Total area of two large triangular faces = 2 x 23.4 in^2 = 46.8 in^2

The area of each of the two small triangular faces is:

Area of triangle = 1/2 x base x height = 1/2 x 5 in x 8 in = 20 in^2

So, the total area of the two small triangular faces is:

Total area of two small triangular faces = 2 x 20 in^2 = 40 in^2

Therefore, the total surface area of the pyramid is:

Total surface area = Area of base + Total area of two large triangular faces + Total area of two small triangular faces

Total surface area = 30 in^2 + 46.8 in^2 + 40 in^2

Total surface area = 116.8 in^2

Answer:

Yes

Step-by-step explanation:

the factors of (x^ 2 +9x+20) are (x+4)(x+5)

The least number of distinct values that can occur in the list is 225.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.

The mode appears 10 times. That leaves 2008 numbers.

The least number of distinct values will occur if all but one of the remaining values appears 9 times

= 2008/9

=223 1/9.

So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.

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Answer:

$21.96

Step-by-step explanation:

Total money with Mr. Rosas = $90

Total cost of chips = 36*0.69 = $24.84

Total cost of juices = 36*1.20= $43.2

Total money spent = $24.84 + $43.2 = $68.04

Money left with Mr. Rosas

= $90 - $68.04

= $21.96

Answer:

a. C(x) = $3.50 + $0.10x. b. distance traveled c. cost of the taxi ride d. $0.10 per mile

Step-by-step explanation:

A. Let C be the cost of the taxi ride and x be the distance traveled in miles. Since there is a base charge of $3.50 and a charge of $0.10 per mile, the cost of the ride is thus

C(x) = $3.50 + $0.10x.

B. The independent variable represents the distance traveled in miles since it is the parameter being measured.

C. The dependent variable represents the cost of the taxi ride, since it is value depends on the parameter (the distance) being measured.

D. The rate of change in this scenario is the $0.10 per mile

Answer A is the only one that seems to make sense to me id choose A

a and d are true statement

ok as know to me

Answer:

30

Step-by-step explanation:

15 - 20

13 - 10

20+10=30

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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Answer:

y = 3x + 11

Step-by-step explanation:

obviously since y is 11 when x is zero the constant term is 11.

Then use the other coordinates to find the cooefficent of x.

-4= c × -5 + 11

-4= -5c + 11

5c=15, c=3

Therefore the equation should be:

y= 3x + 11

The function that best represented by this graph is f(x) = −x² + 1.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

A graph of a function is given in the image.

The parent function of the graph is g(x) = x².

And the graph is negative of the parent function.

And shifted upwards to 1 point.

That means, the function is f(x) = −x² + 1.

Therefore, the function is f(x) = −x² + 1.

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1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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Answer:

they are 4 i think

Step-by-step explanation:

5 x 4 = 20

Answer:

100

Step-by-step explanation:

20 divided by 1/5 = 20 x 5/1 = 100

Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 and divide it by 3, since the crew is finishing 3 km per week. You get 6.25, so it took the crew 6.25 weeks to finish the road.

Hopefully this helps- let me know if you have any questions!

Answer:

Corresponding parts are congruent

Congruent parts:

Sides

Angles in simple form

Angles in full format

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

Congruent parts:

Sides

Angles in simple form

Angles in full format

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

Congruent parts:

Sides

Angles in simple form

Angles in full format

9514 1404 393

Answer:

Step-by-step explanation:

The key with naming corresponding parts is to use the congruence (or similarity) statement. Corresponding vertices are those that are in the same position in the congruence statement, regardless of what the figure may look like.*

Angles can be named using the letter at its vertex--if there is only one angle with that vertex--or using three letters. The three letters name a point on one ray, the vertex, and a point on the other ray. When naming corresponding angles from a congruence statement, it is nice (but not absolutely essential) to name the corresponding rays in the same order. In any event, the named vertices must be corresponding.

Sides are named using two letters--the points at the end of the side. The points used to name corresponding sides must come from the same positions in the congruence statement. Technically, side named AB is the same as side BA, but it is nice to use corresponding points in the same order when naming corresponding sides. Example: in the first figure, CB≅JK, but it is also true that BC≅JK because CB can be named either as CB or BC. In both cases, the points named are the 1st and 2nd in the congruence statements.

In the answer section above, we have used 3-letter angles where a vertex is shared by two or more angles. We have used single-letter names for angles where there is no ambiguity. When asked to name all the names, as here, it is best to make use of a pattern you understand. For angles, we worked left-to-right down the congruence statement; for sides we used the pattern 12, 13, 23 for the positions of the letters in the congruence statement.

_____

* Sometimes, poorly-edited curriculum materials will misstate the congruence statement. It is best to report the problem to your teacher in those cases. Sometimes, the figure is intentionally misleading (as in the second problem here). For those, you must pay careful attention to the congruence statement.

The graph g(x) is the graph of the function Rx) translated 2 units to the left and 6 units up.

g(x) can be represented as:

g(x) = 3(x + 2) + 7

Note that we added 2 inside the parentheses to shift the function 2 units to the left, and added 7 outside the parentheses to shift the function 6 units up.

To find the relationship between the function R(x) = 3x + 1 and the graph of g(x), we need to determine the translation of R(x) that results in g(x). Since the given information about g(x) is limited, I will assume that the graph of g(x) has a y-intercept at (0, 2) and the slope is the same as R(x).

R(x) has a y-intercept at (0, 1), and g(x) has a y-intercept at (0, 2). This means that the graph of R(x) has been translated 1 unit upwards to obtain the graph of g(x). Therefore, g(x) can be expressed as:

g(x) = 3x + 1 + 1 = 3x + 2

In conclusion, the graph g(x) is the graph of R(x) translated 1 unit upwards, and g(x) = 3x + 2.

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The length of Diagonal is 14.73 unit.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Given:

l = 9, w= 10 and h= 6

The Formula for Diagonal length of Prism is:

d =√l² + w² + h²

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Substitute the value in the equation,

d =√9² + 10² + 6²

d =√81+ 100 + 36

d = √217

d =  14.73 units

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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The answer is B. Normal. For a normal distribution, the mean, median, and mode are all equal to each other.

- Mean: The mean of a normal distribution is the center of the distribution, which is also the highest point of the bell-shaped curve.

- Median: The median of a normal distribution is the same as the mean, since the distribution is symmetric around the center.

- Mode: The mode of a normal distribution is also the same as the mean and median, since the highest point of the curve (i.e. the mode) is at the center of the distribution.

For the other probability distributions:

- A. Uniform: A uniform distribution has no mode (or multiple modes), and the mean and median are equal but different from the mode (if it exists).

- C. Exponential: An exponential distribution has a mode of 0, a median of ln(2)/λ, and a mean of 1/λ. Therefore, the mean, median, and mode are not equal.

- D. Poisson: A Poisson distribution has a mode of the integer part of λ (i.e., the highest probability mass function value). The mean and median are both equal to λ. Therefore, the mode is not necessarily equal to the mean and median.

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Answer:

OC

Step-by-step explanation:

I got it right on my test!

Answer:

Rs 6000

Step-by-step explanation:

To find the original price of the article, we need to reverse the effect of the 30% price reduction. We can do this by dividing the sale price of 4200 by the discounted price of 70%, which is equal to 0.7.

The original price is equal to:

4200 / 0.7 = <<4200/0.7=6000>>6000

So the original price, or the marked price, of the article is Rs 6000.

The diagonal of a room measuring 5 ft and 12 ft along the walls should be 14.6 ft.

The diagonal of the room can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse would be the diagonal, the other two sides would be 5 ft and 12 ft.

Thus, the equation would be: a² + b² = c², with a = 5 ft, b = 12 ft, c = 14.6 ft.

The calculation for this equation is as follows:

5² + 12² = c²; 25 + 144 = c²; 169 = c²; √169 = c; c = 14.6 ft.

This means that the diagonal of a room measuring 5 ft and 12 ft along the walls is 14.6 ft.

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Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by \(D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$\).

Therefore,

A = \((x_{1} , y_{1} )\) = (3, 2), B = \((x_{2} , y_{2} )\) = (-2, -3)

\(& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}\)  units

B = \((x_{1} , y_{1} )\) = (-2, -3), C = \((x_{2} , y_{2} )\) = (2, 3)

\(& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}\)  units

A = \((x_{1} , y_{1} )\) = (3, 2), C = \((x_{2} , y_{2} )\) = (2, 3)

\(& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}\)  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

\(& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\\)

\(& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2\)

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

Answer:

3.25

Step-by-step explanation:

total 18.25 - 2.00 tip = 16.25

16.25/5=3.25

We have a function:

The number of bottles of soda is  4 and the number of bottles of juice purchased is  8.

We know that linear system of equation in two variables is required to solve the problem. Let suppose number of bottles of soda purchased by Jacob is x and number of bottles of juice purchased by Jacob is y

Since, it is given that Jacob bought 25 bottles in total, it means

=>x + y=12-----(eq1)

Also, it is given that total amount of sugar is 240grams.Now,amount of sugar present in soda bottle is 25x and amount of sugar present in juice bottles is 12y

Therefore,25x + 12y=240-----(eq2)

On solving eq1 and eq2,we get

=>x+y=12

and 25x+10y=240

Using elimination technique to solve, make x terms coefficient equal.

Multiplying eq1 by 25,we get

=>25x + 25y=25×12

=>25x +25y=300------(eq3)

Using eq3 and eq4,we get

=>25x+25y=300

and 25x+10y=240

Cancelling x terms, we get

=>15y=60

=>y=(60/15) grams

=>y=4 bottles

Now, putting value of y in eq1 ,we get

=>4+y=12

=>y=12-4

=>y=8bottles.

Hence, required value of number of bottles of soda is 4 and number of bottles of juice is 8.

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Answer:

8.20in³

Step-by-step explanation:

Given V = πr²h

r is the radius = 1.5in

h is the height = 6in

thickness of wall of the cylinder dr = 0.04in

top and bottom thickness dh 0.07in+0.07in = 0.14in

To compute the volume, we will find the value of dV

dV = dV/dr • dr + dV/dh • dh

dV/dr = 2πrh

dV/dh = πr²

dV = 2πrh dr + πr² dh

Substituting the values into the formula

dV = 2π(1.5)(6)•(0.04) + π(1.5)²(6) • 0.14

dV = 2π (0.36)+π(1.89)

dV = 0.72π+1.89π

dV = 2.61π

dV = 2.61(3.14)

dV = 8.1954in³

Hence volume, in cubic inches, of metal in the walls and top and bottom of the can is 8.20in³ (to two dp)

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer:

A) 12-10

B)36+225

Step-by-step explanation:

A) 3x4=12, 5x2= 10= 12-10

B) 3x2=6x6=36, 3x5=15x15=225=36+225

For x = 3 and y = 5 the values of the given expressions are (a) 4x - 2y = 2 and (b) 2x² + 3y² = 93.

Substitution is a mathemaical technique for replacing variables with specific or covnient values according to the context.

When the values of variables are given to solve an equation we just have to replace those numerical values in place of the given variables.

Given, x = 3 and y = 5.

∴ 4x - 2y is,

= 4(3) - 2(5).

= 12 - 10.

= 2.

And

2x² + 3y².

= 2(3²) + 3(5²).

= 2(9) + 3(25).

= 18 + 75.

= 93.

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The complex number in polar form with argument θ between 0 and 2π is

θ = 6√2 (cos 7π/4 + i sin7π/4).

What is polar form of complex number?

Another method of expressing a complex number is in its polar form. A complex number's rectangular coordinate form is represented by the formula z = a + bi.

As per question given that,

Complex number: z = 6 - 6i

Polar form is given by IzI (cosθ + i sinθ).

So, evaluate the value of IzI as follows:

IzI = √((a)² + (b)²)

Substitute values respectively,

IzI = √((6)² + (-6)²)

IzI = √(36 + 36)

IzI = √(72)

IzI = 6√2

And evaluate the angle as follows:

θ = arc tan (-b/a)

Substitute values respectively,

θ = arc tan (-6/6)

θ = arctan (-1)

θ = 2π - π/4

θ = 7π/4

Hence, the polar form is,

θ = IzI (cosθ + i sinθ)

Substitute obtained values,

θ = 6√2 (cos 7π/4 + i sin7π/4)

Hence, the complex number in polar form with argument θ between 0 and 2π is θ = 6√2 (cos 7π/4 + i sin7π/4).

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