Determine whether y varies directly with x. If so, find the constant of variation and write the equation. x=-2,-4,-16 y= -4, -8, -32

To convert a fraction to a decimal, we simply divide.

Shown below:

This is never ending decimal with the "6" repeating.

Thus, we can put a bar over "6".

So,

Answer:

Step-by-step explanation:

Exact Form:

1/2

Decimal Form:

-0.5

Answer:

- 2

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{\frac{1}{7} }[/tex] 49 = n , then

49 = [tex](\frac{1}{7}) ^{n}[/tex]

49 = [tex](7^-1)^{n}[/tex] , that is

7² = [tex]7^{-n}[/tex]

since bases on both sides are equal then equate exponents

- n = 2 ( multiply both sides by - 1 )

n = - 2

Answer: The length of the edge of the crate is 3 feet.

Step-by-step explanation:

The formula of the volume of a cube is the cube of edge length.

The volume of the cube (V) = (edge)³ ...................................(1)

In the given question volume is 27 cubic feet.

So, V = 27 cubic feet

Now we replace the Volume with the edge using equation (1)

i.e. (edge)³ = 27

or we can say that the cube root of the edge is equal to 27

i.e. edge = ∛27

which is equal to 3

hence, edge = 3 feet

To calculate the cube root write prime factors of 27 and group them in groups of three

i.e. ∛27 = ∛(3×3×3) = ∛ (3)³ = 3

The rectangular sign is 30 feet in length and 42 feet in width.

The perimeter of the rectangular sign = 144 ft

Let the width of the rectangular sign be x, and the length of the sign will be x-12

The formula for the perimeter of the rectangle:

P = 2(l+w)

where P = perimeter of the rectangle

l = length of the rectangle

w = width of the rectangle

Substituting the values in the formula we get:

144 = 2(x-12+x)

144 = 2(2x-12)

144 = 4x -24

168=4x

x= 42

So, the length is 30ft and the width is 42ft

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From Option 1,2,3 and 4.

Option 3 transformation is A dilation does not always preserve distance.

Give that,

We have to find which transformation does not always preserve distance.

1 (x,y) → (x + 2, y)

2 (x,y) → (-y, -x)

3 (x,y) → (2x, y - 1)

4 (x,y) → (3-x, 2-y)

Option 3 is A dilation does not always preserve distance.

Dilation means a modification of this kind that alters the size of the image is called a dilatation. How much larger or smaller the image is is determined by the scale factor, often known as the scalar factor. A picture of each type of dilatation is shown below (one that gets larger and one that gest smaller).

Therefore, Option 3 transformation is A dilation does not always preserve distance.

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Answer:

1/24

Step-by-step explanation:

Answer:

1/24

Step-by-step explanation:

so first you cross out the 2 and 16 because 2*8=16

then you multiply the numerator and the denominator.

then bam! your answer!

1/24

Using the alternate exterior angles theorem, the value of x is: 127°.

When two parallel lines are intersected by a transversal to form alternate exterior angles that lie outside on each of the parallel lines, the alternate exterior angles theorem states that both angles are equal or congruent to each other.

From the diagram given, we are told that line m is parallel to line n.  transversal t crosses both lines  and n. The angles, x and 127 degrees are alternate exterior angles that lie on each parallel lines.

Therefore, the alternate exterior angles theorem states that, both angles would be equal.

Thus, we can conclude that, x = 127°.

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Answer:

(1) p(x) = 7x³ + 4x² + 6 - 9x⁴

(2) p(x) = 1 + 3x - 9x⁵

(3) y = 9x² - x³ + x⁹

(4) f(x) = (x +3)(x-2)(x+5)

Step-by-step explanation:

Standard form has terms arranged from the highest to the lowest power

Degree is the highest power

Leading coefficient is the coefficient of the highest term

Leading term is the term containing the highest power

(x + 3) (x - 2)(x + 5)

(x + 3) (x - 2) = x² + x - 6 using the FOIL method
(x² + x - 6)(x +5) = x³ + 6x² -x - 30

Step-by-step explanation:

come on, we explained this already in previous questions. if you understood the explanations there, you should have been able to some that here without any problems.

again, standard form is the sorted polynomial from highest variable exponent to the lowest (as the potential constant at the end represents the x⁰ term).

the leading term is the first term on the left (with the highest exponent).

the leading coefficient is the factor in this leading term.

degree is the highest exponent used in the polynomial (again, given by the leading term).

so, what is still the problem ?

i have a slight problem with your handwriting. it is unclear, if there is 7x³ or 17x³. or 13x or 3x.

1.

p(x) = 17x³ + 4x² + 6 - 9x⁴

now, just sort this from the highest to the lowest exponent.

p(x) = -9x⁴ + 17x³ + 4x² + 6

if it should be 7x³ instead of 17x³, please use 7x³ in the polynomial.

degree = 4

leading coefficient = -9

leading term = -9x⁴

2.

p(x) = 1 + 13x - 9x⁵

again sort from highest to lowest exponent

p(x) = -9x⁵ + 13x + 1

again, if it should be 3x instead of 13x, please use 3x in the polynomial.

degree = 5

leading coefficient = -9

leading term = -9x⁵

3.

y = 9x² - x⁵ + x⁹

remember, y = f(x)

that is the same thing, means the same thing. it just gives the result variable a specific name.

again sort by exponent.

y = f(x) or p(x) or ... = x⁹ - x⁵ + 9x²

degree = 9

leading coefficient = 1

leading term = x⁹

4.

f(x) = (x+3)(x-2)(x+5)

this is really like the other question I just answered.

so, we always multiply 2 terms. that result we multiply by the third term. and if they're are more, then that result with the fourth term, and that with the 5th term,...

I usually start at the left :

(x+3)(x-2) = x² - 2x + 3x - 6 = x² + x - 6

now

(x² + x - 6)((x+5) = x³ + 5x² + x² + 5x - 6x - 30 =

= x³ + 6x² - x - 30

so,

f(x) = x³ + 6x² - x - 30

degree = 3

leading coefficient = 1

leading term = x³

Given the following functions:

to find f(g(4)), we can start by finding g(4) first:

now that we know that g(4) = 8, we can calculate the composition f(g(4)):

Answer:

f(g(4) ) = 31

Step-by-step explanation:

evaluate g(4) then substitute the value obtained into f(x)

g(4) = [tex]\frac{4^2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 , then

f(8) = 3(8) + 7 = 24 + 7 = 31

Information regarding various dogs' masses is displayed in the table.

(a) 4 bare minimum number of dogs that could weigh more than 27 kg.

(b) 17 dogs, in total, may weigh more than 27 kg.

Given that,

Information regarding various dogs' masses is displayed in the table.

(a)Calculate the bare minimum number of dogs that could weigh more than 27 kg.

(b)Calculate how many dogs, in total, may weigh more than 27 kg.

(a) 4 bare minimum of dogs that could weigh more than 27 kg.

Because the minimum number so lets assume that all dogs in 20≤x<30 are less then 27.

Therefore, 4 bare minimum of dogs that could weigh more than 27 kg.

(b) 17 dogs, in total, may weigh more than 27 kg.

Because the maximum number so lets assume that all dogs in 20≤x<30 are more then 27.

4+13=17

Therefore,17 dogs, in total, may weigh more than 27 kg.

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Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{50}[/tex] × [tex]\sqrt{8}[/tex]

= [tex]\sqrt{50(8)}[/tex]

= [tex]\sqrt{400}[/tex]

= 20

The integer values of x in the interval 3 ≤ x ≤ 9 that will satisfy the inequality include 3, 4, 5, 6, 7, 8, and 9.

It should be noted that an integer is simply used to represent a given number which can be positive.

From the information, we are given the information 3 ≤ x ≤ 9. This means that 3 is less than or equal to x and x is less than or equal to 9.

Therefore, the number that fits are from 3 to 9.

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27/4 , -3.2, -∛60 ,√48, 7.05 when arranged in ascending order we get:

-3.2 , -∛60 , 27/4 , √48, 7.05

Given list of numbers,

27/4 , -3.2 , -∛60 , √48 , 7.05.

simplifying each numbers ,

=> 27 / 4 = 6.75

=> -∛60 = - ∛(2 × 2 × 3 × 5)

= -3.9149.

=> √48  = √(2 × 2 × 2 × 2 × 2)

= 4√3

= 6.928  

So the list after simplification is ,

6.75 , -3.2 , -3.9149 , 6.928 , 7.05

Now arrange the numbers from least to greatest,

-3.2 , -3.91 , 6.75 , 6.928 , 7.05  

= -3.2 , -∛60 , 27/4 , √48, 7.05.

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The value of the expression 253×67 using the turtle method is given by 16951.

The turtle method of multiplication was designed in order to make the multiplication of larger numbers easier. The larger numbers can be multiplied imagining them as the form of a turtle's head and neck. It involves mainly three steps of multiplication. The first step includes the multiplication of the numbers lying on the neck of a turtle. The next step includes making the collar of the turtle, taking care of the carryovers, and laying the egg of the turtle. The last step involves the multiplication of the other numbers. In the question, we are given the expression 253×67. We multiply this expression in the turtle method as attached in the figure.

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Based on the fact the game of hearts, four players are each dealt 13 cards from a deck of 52

This is further explained below.

A surjective function is a kind of function that exists in mathematics that ensures that any element y may be transferred to element x in such a way that f(x) equals y.

To put it another way, each element that makes up the function's codomain is the mirror image of at least one element that makes up the domain.

Generally, function, f(k) maps a card to each player

And since each player is dealt 13 cards st 13 of the cards are mapped to each player.

It is a function as one card is mapped to one and only one player.

The function is not injective because 13 cards 1 are mapped to one player so it is a many-one function but the injective function does not map two elements to a common clement.

In conclusion, It is surjective as each player is dealt 13 cards. the function is not injective hence rot bijective.

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Based on the graph given on the height of the helicopter, the slope and y-intercept of the function would be:

To find the slope of the line om the height of the helicopter, the formula is:

= Change in y / Change in x

= (100 - 50) / (5 - 0)

= 50 / 5

= 10

The y-intercept takes the form b in the linear equation model:

y = mx + b

100 = 10(5) + b

b = 100 - 50

b = 50

The slope is 10 and the y-intercept is 50.

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When two straight lines or rays intersect at a single endpoint, an angle exists formed. If 2 and 3 exists complements, and m2= 55°, then m3 = 90 - 55 = 35 degrees.

When two straight lines or rays intersect at a single endpoint, an angle exists formed.  The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Complements sum to 90 degrees.

If 1 and 2 are complements and m1 = 35°, then

m2 = 90 - 35 = 55 degrees.

Now if 2 and 3 are complements, and m2= 55°,

then m3 = 90 - 55 = 35 degrees.

The complete question is:

Given: 1 and 2 are complements, 2 and 3 are complements, and m1 = 35°. Prove: m3 = 35° Complete the missing parts of the paragraph proof. By then, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of angles. Then, using the property, the measure of angle 3 is the degree.

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Answer:

The last answer is correct.

Step-by-step explanation:

The plant start at 4 inches (0,4) and then grows 1 inch each week.

(1,5), (2,6).(3,7) and so on.

The cat rescue must sell 87 beds to meet the goal

The car rescue is selling cat beds as a fundraiser

The goal is to raise $1300

Each cat bed is sold at $15

The number that must be sold to reach the goal can be calculated as follows

= 1300/15

= 86.6

= ≅ 87

Hence 87 cat beds must be sold to reach the goal

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Answer:

(10, -3)

Step-by-step explanation:

It is stated in the given information.

Step-by-step explanation:

don't panic. just breathe and then use common sense.

1.

1 math question in 1/200 second

2 minutes have 2×60 seconds = 120 seconds.

each of the seconds has 200 1/200 seconds.

so, in 2 minutes we have

120 × 200 time units to finish math questions.

in each time unit 1 math question can be answered.

120×200 = 24,000

the computer can answer 24,000 math questions in 2 minutes.

2.

it can run for 15 minutes.

15 minutes have

15×60 = 900 seconds (as every minute has 60 seconds)

it can vacuum 1/2 ft² in 1 seconds.

in 900 seconds it can then vacuum 900×1/2 = 450 ft².

so, yes, it can clean 400 ft² without recharging.

The rate of change is found using the slope formula

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

We have two points

( 1995, 2.54) ( 2010, 3.18)

m = (3.18-2.54) / (2010-1995)

=.64/15

$.042666666 per year

Rounding to the nearest cent

$.04 per year

We know that the price went up from 1995 to 2010 so the price increased

It increased an average of $.04 each year

A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010

13.4 dollars.

This is the total amount Kelly deposit when she opened the account.

Here,

The total amount is determined by:

               F=I(1+rt)

Where

Here given ,

r = 1.2%

t = 7

F = $126

As a result,

I = F/(1+rt)

= 126/1+1.2*7

= 13.4 dollars.

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Answer:

2(5)+2x+2y

Step-by-step explanation:

since you both have the tickets the amount of the prize is going to double. You both also bought popcorn and soda if we take 1 popcorn as "x" it is also going to multiple 2 times same with the soda except different variable.

The expression that represents the given condition is given by

5.75x + 35.

In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

If x shirts are bought, cost of x shirts at $5.75 = 5.75x

Set up fee $ 35

Total cost of x shirts = 35 + 5.75x

Therefore the required expression = 35 + 5.75 x

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Answer: B

Step-by-step explanation: A whole number is a number that is not a decimal or a fraction and is over 0.