What is the rate of change and initial value for the linear relation that includes the points shown in the table? x y 2 3 4 5 6 7 8 9 Initial value: 1, rate of change: 2 Initial value: 1, rate of change: 1 Initial value: 2, rate of change: 2 Initial value: 3, rate of change: 2

Answer:

cos A= 5/13

tan A= 12/5

Step-by-step explanation:

Answer:

cos A= 5/13

tan A= 12/5

Step-by-step explanation:

Your welcome :)

Answer: triangular pyramid

Step-by-step explanation:

Answer:

Triangular Pyramid

Step-by-step explanation:

A triangular pyramid consists of 1 triangular base, with three lateral faces also in the shape of a triangle. Its net consists of 4 triangles, and is a solid 3-Dimensional figure. I hoped this helped.

Answer:

Part a) The Labeled part of the Can ⇒ 263.76 cm^2

Part b) The Surface Area of the Can is ⇒ 340.69 cm^2

Part c) The Volume of the Can is ⇒  38.465 * 12 = 461.58 cm^2

Step-by-step explanation:

~ If the dimensions of this can is 12 centimeters by 7 centimeters... ~

Part a)

1. Now a can is in the shape of a cylinder, thus the Base would act as a circle. That being said, 7 centimeters acts as the diameter of this circle.

2. If we were to unravel the middle of the can, it would be that this circular portion turns out of be a rectangle, with dimensions of the height of the cylinder, by the circumference of the Base of the cylinder. The circumference can be calculated by πd where d is the diameter ⇒ 3.14 * 7 ⇒ 21.98 cm. Thus the dimensions of this middle part of the can is 21.98 by 12 ⇒ 21.98 * 12 ⇒ 263.76 cm^2.

The Labeled part of the Can ⇒ 263.76 cm^2

Part b)

1. We know previously, that 7 centimeters acts as the diameter of this circle, so the radius must be half of that, which is 7/2 ⇒ 3.5 cm. Now we can apply the area of a circle formula πr^2 where r ⇒ radius, such that: 3.14 * ( 3.5 )^2 ⇒ 3.14 * 12.25 ⇒ 38.465 cm^2.

2. Knowing that the Base of this can is 38.465 cm^2, multiply this value by 2 to get the surface area of the two bases, provided they are equivalent: 38.465 * 2 ⇒ 76.93 cm^2

3. We know that this labeled section of the can is ⇒ 263.76 cm^2. This means that The Surface Area of the Can is ⇒ 263.76 + 76.93 = 340.69 cm^2

Part c )

The volume of the can is calculated by Base * height. We know from the previous questions that the Base ⇒ 38.465, and the height was given to be 12 centimeters. This means that The Volume of the Can is ⇒  38.465 * 12 = 461.58 cm^2

Step-by-step explanation:

Putting value of y

6x + 8(-5) = - 22

6x - 40 = - 22

6x = - 22 + 40

6x = 18

x = 18 / 6

x = 3

Answer:

B y = 3x^2 + 12x + 19

Step-by-step explanation:

y = 3(x + 2)^2 + 7

To expand the square of the binomial,

either recall that (a + b)^2 = a^2 + 2ab + b^2, or use FOIL.

y = 3(x^2 + 4x + 4) + 7

y = 3x^2 + 12x + 12 + 7

y = 3x^2 + 12x + 19

Answer: B y = 3x^2 + 12x + 19

Final answer:

After expanding and simplifying the given function, we find that the equivalent function is y = 3x^2 + 12x + 19, which corresponds to option B.

Explanation:

The task is to find the equivalent function to y = 3(x + 2)2 + 7. We'll start by expanding the square and then distributing the 3 across the resultant terms.

First, expand the square: (x + 2)2 = x2 + 4x + 4.

Next, distribute the 3: 3(x2 + 4x + 4) = 3x2 + 12x + 12.

Finally, add the 7 to complete the expansion: 3x2 + 12x + 12 + 7 = 3x2 + 12x + 19.

Therefore, the equivalent function is B y = 3x2 + 12x + 19.

The required length of the diagonal AB would be 8.66 cm.

The formula for the length of the diagonal of a cube follows as

d = √ (L² + W² + H² )

Where H is the height of the cube,  W is the width of the cube and L is the length of the cube

We have been that the dimensions of a cube are as:

The length of the cube (L) = 5 cm

The height of the cube (H) = 5 cm

The width of the cube (W) = 5 cm

d = √ (L² + W² + H² )

d = √ (5² + 5² + 5² )

d = √ (25 + 25  + 25 )

d = √75

d = 8.66

Therefore, the required length of the diagonal AB would be 8.66 cm.

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Answer:

[tex]V= \frac{15}{4}[/tex]

Step-by-step explanation:

To find find the volume of a rectangular prism you need to formula.

V = whl   w is the width, h is the height, and l is the length.

It shows that the length of one box is 1/2 cm

To find the width, multiply 1/2 by 2 because there's 2 boxes

To find the height, multiply 1/2 by 3 because there's 3 boxes going up

To find the length, multiply 1/2 by 5 because there's 5 boxes going across

Now that you have the width, height, and length put them into the formula.

[tex]V = (1)(\frac{3}{2})(\frac{5}{2})[/tex] multiply everything together

[tex]V= \frac{15}{4}[/tex]

The volume of the rectangular prism is 15/4.

In three dimensional space prism is a polyhedron where two ends are similar.

Given we have  the length of one box is 1/2cm.

To find find the volume of a rectangular prism;

volume of rectangular prism = width x height x length.

To find the width,

multiply 1/2 by 2 because there's 2 boxes.

To find the height,

multiply 1/2 by 3 because there's 3 boxes in one column.

To find the length,

multiply 1/2 by 5 because there's 5 boxes  in  one row.

Now,

volume of rectangular prism = 2(length) x 3 (length) x 5 (length)

volume of rectangular prism = 2(1/2) x 3 (1/2) x 5 (1/2)

volume of rectangular prism = 1 x 3/2 x 5/2

volume of rectangular prism = 15/4

Therefore, the volume of the rectangular prism is 15/4.

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Answer:

Step-by-step explanation:

To find the perimeter, you would have to add all the expressions together, so you would get 2x+x+x+y+y+1+y+y

combine like terms and you will get 4x+4y+1

Answer:

B) 42 signifies the hourly rate, and 32 signifies the overhead charge

Step-by-step explanation:

The hourly rate is the amount of money given per hour worked. 42x basically means that for every hour, $42 are given.

As for 32, it is the overhead charge, which isn't paid every hour but rather only once. That is why it has no variable beside it.

Hope this helps!

Answer:

Shannon bought 3 more pounds of apples.

Step-by-step explanation:

5 - 2 is 3.

Answer:

3

Step-by-step explanation:

5-2=3

Answer:

answer is 2:3

Step-by-step explanation:

i solved it including a calculator

Answer:

65 cm =? m

1m =100cm

1cm=1/100m

65cm=65/100m

65cm =0.65m

Answer:

4 ounces.

Step-by-step explanation:

There is 16 ounces in a pound.

1/4 ounces means there is one pound that was cut into 4 pieces and you want to find how many ounces is in one of those pieces.

Since the pound is divided into 4 pieces, we have to do the same with the 16 ounces in that one pound.

16 ounces divided by 4 is 4 ounces.

1/4 of a pound converted into ounces is 4 ounces.

I hope this helped you! :)

Answer:

v= 64cm3

Step-by-step explanation:

a cube with area of 96cm2 has a length of 4 cm

A=L squared x6

96=L2x6

96/6=16

16 square root=4cm

V=l x l xl

V=4x4x4

v=64cm3

Answer:

B. 1.7 in

Step-by-step explanation:

Divide the triangle into 2 congruent right angle triangles

With hypotenuse: 2

Base: 2/2 = 1

Using pythagoras theorem

2² = 1² + h²

h² = 3

h = sqrt(3)

h = 1.732050808

The height of the equilateral triangle is required.

The height of the logo is option B. 1.7 in.

A perpendicular to from one of the vertices of an equilateral triangle bisects the sides into two equal halves.

a = Length of every side of the equilateral triangle = 2 in

b = Length of the bisected length = [tex]\dfrac{2}{2}=1\ \text{in}[/tex]

From the Pythagoras theorem we have

[tex]a^2=h^2+b^2\\\Rightarrow h=\sqrt{a^2-b^2}\\\Rightarrow h=\sqrt{2^2-1^2}\\\Rightarrow h=1.7\ \text{in}[/tex]

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Answer:

x ≓ -1.425806820

Step-by-step explanation:

Answer:

Vertical Asymptotes:  x=-4

Horizontal Asymptotes:  y=1

Answer:

[tex]\theta = 12.16^0.[/tex]

Step-by-step explanation:

Given,

Height = 12.6 m

Object distance from the person = 58.5 m

Angle of depression

[tex]tan \theta = \dfrac{P}{B}[/tex]

[tex]tan \theta = \dfrac{12.6}{58.5}[/tex]

[tex]tan \theta = 0.2154[/tex]

[tex]\theta = 12.16^0[/tex]

Hence, angle of depression is equal to [tex]\theta = 12.16^0.[/tex]

The angle of depression of the person's line of sight to the object on the ground is 12.15°.

The information forms a right angle triangle. The person eyes above the ground is the opposite side of the triangle. The object distance from the building in line of the sight is the adjacent side of the right angle triangle.

Therefore,

using trigonometric ratio,

tan Ф = opposite /adjacent

tan Ф = 12.6 / 58.5

tan Ф = 0.21538461538

Ф = tan⁻¹ 0.21538461538

Ф = 12.1549416972

Ф = 12.15°

angle of depression  ≈ 12.15°

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So they seem to intersect around the 35 year mark, and tree B was planted at year 0, so therefore they intersected 35 years after Tree B was planted.

The x coordinate is years since B is planted.  Looks like the x coordinate of the intersection is about 35 years.

Answer: 35 years

Answer:

C.; Yes

Step-by-step explanation:

A)

The longest thing that can fit along the base of the box is sqrt ( 13^2 + 35^2) = 37.3, which is less than 38, so NO, the baton can't lay flat on a diagonal along the base of the box C. No, because the diagonal is 37.3 inches long.

B) The interior diagonal of the box is sqrt(13^2 + 13^2 + 35^2) = sqrt (1563), which is 39.5, which is greater than 38, so YES, the baton can fit along the interior diagonal of the box.

The number of different ways ten students can line up for lunch is 3,628,800, which is found by calculating the factorial of 10 (10!).

The question asks how many different ways ten students can line up for lunch. This is a problem of calculating permutations without repetition, as each student is unique and once a student takes a place in line, they cannot be in another position at the same time. The formula to calculate the number of permutations for 'n' unique items is n! (n factorial), which is defined as the product of all positive integers from 1 to n.

In this case, 'n' is 10 because there are 10 students. Therefore, the calculation is 10! =  3,628,800 different ways.

Answer:

A) Sample Space

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

B)Probability of rolling a 6

10/36

Step-by-step explanation:

Answer:

A.         1         2        3         4       5         6

    1    (1,1)    (1,2)    (1,3)    (1,4)    (1,5)    (1,6)      

    2   (2,1)   (2,2)    (2,3)  (2,4)  (2,5)    (2,6)

    3   (3,1)   (3,2)    (3,3)   (3,4)  (3,5)    (3,6)

    4   (4,1)   (4,2)    (4,3)   (4,4)   (4,5)   (4,6)

    5   (5,1)   (5,2)    (5,3)  (5,4)    (5,5)   (5,6)

    6   (6,1)   (6,2)    (6,3)  (6,4)    (6,5)   (6,6)

B.  11/36 or 0.3055555

Step-by-step explanation:

1. You can see there are 36 outcomes when rolling the dice.

2. Then you find that there are 11 possible outcomes with at least one 6. (For example 1-6 2-6 3-6.)

3. The chance of rolling at least one 6 in a pair of dice is 11/36.

4. 11 divided by 36 is 0.3055555.

(Though the calculator on Google says 0.305555556.)

Answer:

The polynomial is irreducible.

Step-by-step explanation:

The polynomial 3p²-15pq+20q² can be factored as (p-2q)(3p-10q).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

The polynomial is given as follows:

3p²-15pq+20q²

It is required to find the factorization of the given polynomial.

The greatest common factor (GCF) of the coefficients (3, -15, 20), is 3.

Rewrite the polynomial using the GCF of 3. We get:

3(p²-5pq+6q²)

We need to find two numbers that multiply to 6q² and add to -5pq.

The numbers are -2q and -3p.

Combine the factored quadratic expression with the GCF of 3.

3(p-2q)(p-3q)

Therefore, the correct factorization of the polynomial 3p²-15pq+20q² is 3(p-2q)(p-3q).

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Answer:

Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.

Step-by-step explanation:

The department store was adding sales tax to the bill. Sales tax is a tax on goods and services purchased and is normally a certain percentage added to the buyer's cost.

Solution: 2.36 ÷ $32.00 = 0.0735. Sales tax was charged by the department store at a rate of 7.375%.

Answer: Mr. Smith should pay the department store $32.00 plus $2.36 in sales tax for a total bill of $34.36.

Sales tax rates vary from state to state. Retail sales tax rates are set by the individual states in the United States and vary from 0 to 9% of the sales price. Sales tax is usually the responsibility of the merchant to collect and submit to the state, and stated separately (or implicitly added at the time of the sale) to consumers.

The additional amount Mr. Smith paid is tax.

The amount was determined by calculating 7.4% of the items bought.

Mr Smith. should pay $34.36.

Tax is an amount of money levied by the government or an agency of the government on certain goods and services. Taxes increases the price of a good or service.

In order to determine the tax paid, divide the additional amount paid by the total cost of items purchased.

(2.36 / $32) x 100 = 7.4%

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Answer:

349.2%

Step-by-step explanation:

£256 = 100%

£2.56 = 1%    

£894 = 349.2%

Answer:

70

Step-by-step explanation:

It is made with a combination. Combination of 4 taken from 8, the formula of the combination is as follows:

nCr = n! / (r! * (n-r)!)

In this case 8 is "n" and 4 is "r"

8C4 = 8! / (4! * (8-4))!

8C4 = 8! / (4! * 4!)

8C4 = 40320/576

8C4 = 70

In this way he obtained the answer that is 70

Answer:

1/2 K-3/5

Step-by-step explanation:

2/5K simplifies to 4/10K.  4/10K+1/10K=5/10K.  5/10=1/2.  1/2K

K and 3/5 are not like terms so you can't combine them.  

1/2K-3/5

Answer:

Step-by-step explanation:

add [tex]\frac{2}{5}k[/tex] with [tex]\frac{1}{10}k[/tex]

[tex]\frac{2}{5}k + \frac{1}{10}k = \frac{1}{2}k[/tex]

[tex]\frac{1}{2}k -\frac{3}{5}[/tex]  and this is your answer

Answer:

X-intercepts: (80,0)

y-intercepts: (0,200)

Step-by-step explanation:

(To find the x-intercept, substitut in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. As shown in the pictur)

The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The school band is selling sweatshirts and baseball caps to raise $2000 to attend a band competition.

Sweatshirts cost $25 each and baseball caps cost $10 each.

The equation 25x + 10y = 2000 models this situation.

Where x is the number of sweatshirts sold and y is the number of baseball caps sold.

Then the x-intercept will be

25x = 200

x = 8

The x-intercept will be (8, 0).

And the y-intercept will be

10y = 200

y = 20

The y-intercept will be (0, 20).

The x-intercept and y-intercept of the equation will be (8, 0) and (0, 20).

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Final answer:

A regular hexagon will coincide with itself when rotated by angles of 60 degrees, or multiples of it like 120, 180, 240, 300, and 360 degrees, because these are the angles of rotational symmetry for a hexagon.

Explanation:

A regular hexagon has six sides of equal length and interior angles that are also equal. When a regular hexagon is rotated about its center, there are specific degree measures for which it will fit exactly onto itself, known as the angles of rotational symmetry. Since a full rotation measures 360 degrees and a hexagon has six sides, we can divide 360 degrees by the number of sides to find the smallest angle of rotation that will carry the regular hexagon onto itself.

The calculation is 360 ÷ 6 = 60 degrees. Therefore, a regular hexagon will coincide with itself every 60-degree turn. Other angles that will carry the hexagon onto itself are multiples of 60 degrees: 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees (a full rotation).