Which is equivalent to 3√2
? Select all that apply
Responses

tan 45°
tan 45°

cos 45°
cos 45°

sin 45°
sin 45°

sin 30°
sin 30°

sin 60°
sin 60°

cos 30°
cos 30°

tan 30°

Answer:

22 degree

Step-by-step explanation:

We know

∠1 and ∠2 combined must be 90 degrees. We know angle 2 is 68 degrees.

What is the measure of angle 1?

90 - 68 = 22 degrees

So, angle 1 is 22 degrees.

The resultant vector for her trip is  <-9, 14>, where the units are miles.

Let's define north as the positive y-axis and east as the positive x-axis.

First we know that she goes 9 mileswestand 4 miles north of her house, then that can be represented by the vector:

<-9, 4>

Then she travels at a speed of 30mi/h for 20 minutes, we know that:

1hour = 60min

then:

20 min = (20/60) hours = (1/3) hours.

The distance that she travels in that time is:

d = (30 mi/h)*(1/3)h = 10 mi

So she travles 10 miles north, this time the vector is <0, 10>

To get the resultant vector we just need to add the two ones we have:

<-9, 4> + <0, 10>  = <-9 + 0, 4 + 10> = <-9, 14>

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Answer:

To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:

10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)

Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:

2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)

= 2x²(5x^2(x + 2) - 2(x + 2))

= 2x²(5x^2 - 2)(x + 2)

Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).

Step-by-step explanation:

Answer: I'd be happy to help you with these problems!

1a.

i. Cardinal: There were 10 apples in the basket.

ii. Ordinal: He came in first place in the race.

iii. Nominal: My favorite color is blue.

i. 1997 in Roman numerals is MCMXCVII.

ii. 15-03-2023 in Roman numerals is XV-III-MMXXIII.

2a.

2√128 - √243 + 5√125 + √27 - √80 - 162 + √98

First, simplify the square roots:

2√64·2 - 3√81·3 + 5√25·5 + √9·3 - √16·5 - 162 + √49·2

Next, simplify further:

2·8√2 - 3·3√3 + 5·5√5 + 3√3 - 4√5 - 162 + 7√2

Combine like terms:

15√2 - √3 + 8√5 - 162 - 4√5 + 7√2

Simplify further:

22√2 + 4√5 - √3 - 162

b.

1.3555555555.... can be written as 1.36 in 7º.

c.

Village A has a funeral every 10 days, so it will have a funeral on March 4th, March 14th, March 24th, etc.

Village B has a funeral every 15 days, so it will have a funeral on March 4th, March 19th, April 3rd, etc.

Village C has a funeral every 20 days, so it will have a funeral on March 4th, March 24th, April 13th, etc.

To determine the next time all three villages will have a funeral on the same day, find the least common multiple of 10, 15, and 20.

10 = 2 x 5

15 = 3 x 5

20 = 2 x 2 x 5

The least common multiple is 2 x 2 x 3 x 5 = 60.

So, the next time all three villages will have a funeral on the same day is 60 days after March 4th, which is May 3rd, 2023.

Comment if you have any more questions.

The width of the rectangular tile is obtained to be 11 and 2/3 cm.

What is a rectangle?

A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.

The bathroom tile is in a rectangular shape.

Let's call the width of the tile "w".

From the problem, we know that -

w = (2 and 1/3) × h

We also know that the height of the tile is 5 cm.

Substituting this value in the equation above, we get -

w = (2 and 1/3) × 5 cm

w = 7/3 × 5 cm

w = 35/3 cm

w = 11 and 2/3 cm

Therefore, the width of the tile is 11 and 2/3 cm.

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"Given that they passed the test" says we're only considering the 21 students who passed the test.

There were 9 students who didn't pass the test and 7 of those didn't complete the HW.  This means that 2 students who did the HW didn't pass the test.  

Since 20 students completed the HW and 2 didn't pass the test, 18 students completed the HW and passed the test.

18/21 = 6/7 or 85.71%

Your probability is 85.71%.

-3 is not an irrational number, but it is a real number, a rational number, an integer, and a whole number.  

What are whole numbers and rational numbers?

All numbers, including integers, fractions, decimals, and irrational numbers, that can be represented on a number line are considered real numbers.

In summary, real numbers include rational and irrational numbers, and integers include whole number and their negatives.

When two integers are compared, a number can be stated as a ratio, such as -3/1, 1/2, or 5/7. Writing rational numbers as recurring or ending decimals is an option.

Numbers that can't be stated as a ratio of two integers, like 2 or, are referred to as irrational numbers. It is impossible to write irrational numbers using repeating or ending decimals.

Positive and negative whole numbers, as well as zero, are considered integers. Since whole numbers are non-negative integers, they contain zero and only positive values.

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The longest amount of time that Marco could use his phone without changing the battery is given as follows:

3.3 hours.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In 5 hours, the battery fell from 50% to 20%, hence the slope is given as follows:

-30/5 = -6% an hour.

The battery is currently at 20%, hence the time that Marco could use the phone without charging it is given as follows:

20/6 = 3.3 hours.

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Answer:

7p(p-3) (if you're trying to find P then p is 3)

Step-by-step explanation:

First multiply the bottom so you get 9p^2 - 72p and then you can remove 1 variable of p from the bottom and top to get 63(p^3-11p^2+24p) and take one p out for 63p(p^2-11p+24) and factor for 63p(p-8)(p-3)/9(p-8) and take p-8 out of both. Then, you're left with 63p(p-3)/9 to get 7p(p-3) and to solve for p if the equation is equal to 0 -> 7(p)(p-3) = 0

-> 7p^2-21p

->7p^2 = 21p

7p = 21

p = 3

Answer:

Diane got 2 pounds of sugar per dollar.

To see why, divide the number of pounds of sugar by the cost in dollars:

10 pounds / $5 = 2 pounds/dollar

Answer:

1385 square feet

Step-by-step explanation:

42ft÷2=21ft to get the radius

21^2=441ft

441×π=441π

441π=1385.44236

=1385 to the nearest whole number

The rules that are functions on an appropriate domain are A and D, and other solutions are shown below

Given that

g(x) = 4x² + x + 7

For g(-2), we substitute -2 for x in g(x) = 4x² + x + 7

So, we have

g(-2) = 4(-2)² + (-2) + 7

Evaluate

g(-2) = 21

Here, we have

A(t) = 3- 2t² + 4^t.

To calculate A(2) - A(1), we calculate A(2) and A(1) and then subtract the values

So, we have

A(2) = 3 - 2(2)² + 4² = 11

A(1) = 3 - 2(1)² + 4¹ = 5

So, we have

A(2) - A(1) = 11 - 5

A(2) - A(1) = 6

Here, we have

g(x) = 3(x - 6)² + 1

The vertex above is

vertex = (6, 1)

Because the leading coefficient (a) is greater than 0

i.e. a = 3, then the vertex is a minimum

So, the range is y ≥ 1

Here, we have the following definition

a ♡ b = (a + b)/2.

This means that

(5 ♡ 7) ♡ 11 = (5 + 7)/2 ♡ 11

(5 ♡ 7) ♡ 11 = 6 ♡ 11

So, we have

(5 ♡ 7) ♡ 11 = (6 + 11)/2

(5 ♡ 7) ♡ 11 = 8.5

The rules that are functions on an appropriate domain are A and D.

Rules B, C, E, and F are not functions on an appropriate domain

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Complete question

Let g(x) = 4x^2 + x + 7. Find g(-2)

Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).

Let g(x) = 3(x - 6)^2 + 1. Find the range of g. Write your answer in interval notation.

Define the operation ♡ so that a ♡ b = (a + b)/2.

Find the value of (5 ♡ 7) ♡ 11

Which of these rules are functions on an appropriate domain?

Select all that apply.

A inputs a real number, subtracts 100, then outputs the square root of the result if it is real.

B inputs a date, then outputs the name of a person born on that date.

C inputs a real number x, then outputs a real number y that is less than 1/1000 larger than x

D inputs a real number x, then outputs the result of the calculation (x^2-1)/(x-1)(x+1)

E inputs a real number x, then a coin is flipped. If the coin flips heads, the output is x+2. If the coin flips tails, the output is x+3.

F inputs a person, then outputs their birth date.

The height of this container if it is a cylinder with a radius of 3 cm is equal to 5 cm.

The cost of coffee is equal to $2.83.

The height of this container if it is a cylinder with a radius of 5 cm is equal to 1.8 cm.

The cost of hot chocolate powder is equal to $9.90.

In Mathematics, the volume of a cylinder can be determined by using the following formula:

Volume of a cylinder, V = πr²h

Where:

By choosing a volume of 45π cm³, the height of this container can be calculated as follows:

h = V/πr²

Height, h = 45π/π3²

Height, h = 5 cm.

For the cost of coffee, we have:

Cost of coffee = 45π cm³ × $0.02

Cost of coffee = $2.83.

When radius, r = 5 cm, the height of this container is:

h = V/πr²

Height, h = 45π/π5²

Height, h = 1.8 cm.

For the cost of the hot chocolate powder, we have:

Cost of the hot chocolate powder = 45π × $0.07

Cost of the hot chocolate powder = $9.90.

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The correct option is (e) i.e. 3.0.

What are Units ?

In math, units refer to a standard of measurement used to quantify a quantity. Units are used to specify the magnitude of a physical quantity or measurement, such as length, mass, time, temperature, and so on.

The use of units is important in math and science because it allows us to communicate and compare measurements effectively. Without units, it would be difficult to understand or compare different measurements, as they would lack a common reference point.

According to the United States Environmental Protection Agency (EPA), transportation is the largest contributor to greenhouse gas emissions in the United States, responsible for approximately 29% of total greenhouse gas emissions in 2019. In comparison, agriculture accounted for approximately 10% of total greenhouse gas emissions in the same year.

Therefore, for every pound of warming gas produced by agriculture, approximately 2.9 pounds of warming gas are produced by transportation.

So, the closest option from the given choices is 3.0.  

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Answer: 1407.4

Step-by-step explanation:

Tο find the cοst οf 10 such pencils, we need tο multiply the price οf οne pencil by 10. We can write 1½ as a mixed number οr as an imprοper fractiοn.

A prοpοrtiοn is an equatiοn that sets twο ratiοs at the same value. Fοr instance, yοu cοuld express the ratiο as fοllοws: 1: 3 if there is 1 bοy and 3 girls (fοr every οne bοy there are 3 girls) There are 1 in 4 bοys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

A mixed number is a whοle number and a fractiοn tοgether, such as 1½. An imprοper fractiοn is a fractiοn where the numeratοr (tοp number) is larger than the denοminatοr (bοttοm number), such as 3/2. Tο multiply a mixed number by a whοle number, we can either cοnvert the mixed number tο an imprοper fractiοn first, οr multiply the whοle number by the whοle part and the fractiοnal part separately and then add them tοgether. Fοr example:

1½ × 10 = (1 + ½) × 10 = (1 × 10) + (½ × 10) = 10 + 5 = 15

Or

1½ × 10 = (3/2) × 10 = (3 × 10) / 2 = 30 / 2 = 15

Either way, we get the same answer: The cοst οf 10 such pencils is 15.

Tο find the cοst οf 20 such pencils, we can use the same methοd but multiply by 20 instead οf 10. Fοr example:

1½ × 20 = (1 + ½) × 20 = (1 × 20) + (½ × 20) = 20 + 10 = 30

Or

1½ × 20 = (3/2) × 20 = (3 × 20) / 2 = 60 / 2 = 30

Either way, we get the same answer: The cοst οf 20 such pencils is 30.

Tο check if the price is directly prοpοrtiοnal tο the number οf pencils, we need tο see if the ratiο οf the price tο the number οf pencils is cοnstant. A ratiο is a cοmparisοn οf twο quantities using divisiοn. A cοnstant ratiο means that nο matter hοw many pencils we buy, the price per pencil will always be the same. Fοr example:

Price / Number οf Pencils = Cοnstant Ratiο 15 / 10 = Cοnstant Ratiο 30 / 20 = Cοnstant Ratiο

We can simplify these fractiοns by dividing bοth numbers by their greatest cοmmοn factοr (GCF). The GCF οf 15 and 10 is 5, sο we divide bοth numbers by 5:

(15 / 5) / (10 / 5) = Cοnstant Ratiο 3 / 2 = Cοnstant Ratiο

The GCF οf 30 and 20 is alsο 5, sο we divide bοth numbers by 5:

(30 / 5) / (20 / 5) = Cοnstant Ratiο 6 / 4 = Cοnstant Ratiο

Nοw we can cοmpare these simplified fractiοns and see if they are equal. If they are equal, then it means that the price per pencil is always the same regardless οf hοw many pencils we buy. If they are nοt equal, then it means that the price per pencil changes depending οn hοw many pencils we buy.

3 /2= ?6 /4 12 /8= ?12 /8 12 /8=12 /8

Since these fractiοns are equal, it means that:

Price / Number οf Pencils = Cοnstant Ratiο Price ∝ Number οf Pencils

The symbοl ∝ means “is prοpοrtiοnal tο”. Sο this equatiοn tells us that yes, the price is directly prοpοrtiοnal tο the number οf pencils because fοr every increase in οne unit in οne quantity (number οf pencils), there is a cοrrespοnding increase in a fixed amοunt in anοther quantity (price).

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Answer: 64x

Step-by-step explanation:

Subtract 6 from 20 to get 14.

Multiply 14 and  1/2 to get 14/2

Divide 14 by 2 to get 7.

Add 1 and 7 to get 8.

Multiply 8 and 8 to get 64.

​

.

Therefore , the solution of the given problem of equation comes out to be  Y is equally distant from X and Z.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces a + 7 as opposed to a different algorithm that splits 12 into two parts and can evaluate data received from x + 7.

Here,

We can infer from the knowledge that

=> PQ = XZ

because X, Y, and Z are equally spaced apart from P and Q.

Based on this knowledge alone, we cannot infer that X, Y, and Z are collinear or that Y is equally distant from X and Z.

Therefore , the solution of the given problem of equation comes out to be  Y is equally distant from X and Z.

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The algebraic expression that represents the verbal expression is given as follows:

(j + m)/7.

The algebraic expression representing the situation is obtained applying the proportions in the context of the problem.

The verbal expression is given as follows:

"Jaylen brought j crackers and combined them with Marvin’s m crackers. They then split the crackers equally among 7 friends.".

The total number of crackers is then given as follows:

j + m.

The crackers were divided evenly among the seven people, hence the expression representing the number of crackers by each person is obtained applying the proportion as follows:

(j + m)/7 -> total divided by number of people.

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Answer: The given equation of the line is y + 2 = -1/2 x, or equivalently, y = -1/2 x - 2. This equation is in slope-intercept form, y = mx + b, where the slope m is -1/2.

A line parallel to this line will have the same slope, so its equation will also be in the form y = -1/2 x + b, where b is the y-intercept that we need to find.

To find b, we can use the fact that the line passes through the point (2, -7). Substituting x = 2 and y = -7 into the equation, we get:

-7 = -1/2 (2) + b

Simplifying and solving for b, we get:

b = -7 + 1 = -6

Therefore, the equation of the line parallel to y + 2 = -1/2 x that passes through the point (2, -7) is:

y = -1/2 x - 6

Step-by-step explanation:

Answer:

5.91

Step-by-step explanation:

formula of a circle = (x-h)^2 +*y-k)^2 = r^2

thus, to get the radius, square root 35 which when rounded two deicmal places is 5.91

The evaluation of the probability of picking the real numbers can be presented as follows;

(a) The probability of picking a real number between 3 and 5 is 0.57

(b) The probability that a real number between 3 and 7 is picked is; 0.88

The probability of an event is the ratio of the number of required outcome to the number of possible outcome

The area in each region are;

Area under the curve of region A = 0.12

Area under the curve of region B = 0.56

Area under the curve of region C = 0.36

The probability that an event occurs can be taken as the ratio of the area under the curve, and the entire area, therefore;

(a) The probability that a real number between 3 and 5 is picked, can be found as follows.

(b) The area of the region under the curve between 3 and 7 includes the region between 3 and 5 and between 5 and 7, therefore;

The area between 3 and 7 = Area between 3 and 5 + Area between 5 and 7

The area between 3 and 7 = 0.56 + 0.32 = 0.88

The probability of that a real number between 3 and 7 is picked, therefore can be obtained as follows;

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Answer: 3a^5b

Step-by-step explanation:

I just did an exam with the question, and I got it correct.

Answer:

Like the other person said, C.

Step-by-step explanation:

also got it correct on the test

have a good day xx

The length of one side of the box is approximately 8.5 inches whose circumference is 37.7 inches.

Circumference is the distance around the edge of a circle or any circular object. It can be found by multiplying the diameter of the circle by pi (π), which is approximately 3.14159. Alternatively, it can be found by multiplying twice the radius of the circle by pi.

The diameter of the circle inscribed in the square is equal to the side length of the square. Since the circumference of the pizza crust is 37.7 inches, the diameter of the circle is:

d = circumference / pi = 37.7 / pi ≈ 12

Therefore, the radius of the circle is r = d/2 ≈ 6. To find the side length of the square, we need to find the diagonal of the square, which is equal to twice the radius of the circle. As a result, the square's length of one side is:

s = diagonal / √(2) = 2r / √(2) = 6 √(2) ≈ 8.5

Therefore, the length of one side of the box is approximately 8.5 inches.

The circumference is an important measurement in geometry and is used to calculate the perimeter of circles, as well as to determine the length of curved lines in various other contexts.

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Answer:

For a polygon to be regular, it must satisfy the following two conditions:

All of its interior angles must be congruent.

All of its sides must be congruent.

Let n be the number of sides of the polygon. Then the measure of each interior angle of a regular n-gon is given by:

180(n-2)/n degrees

For a 25-gon, the measure of each interior angle is:

180(25-2)/25 = 156.8 degrees

Therefore, option D) "All interior angles and all sides are congruent" must be true for a 25-gon to be regular.

Answer: 19 units

Step-by-step explanation:

Just subtract the y values and find the absolute value since the x values are the same.

The y-intercept of the equation is -10.

Equation is a mathematical statement that expresses the equality of two expressions, which are separated by an equals sign. It can be used to represent a variety of different relationships, such as equality, inequality, addition, subtraction, multiplication, and division. Equations can be used to solve a variety of problems in science, engineering, and mathematics.

The x-intercepts of the graph of the equation r(x) are those values of x for which the equation is equal to 0. To find the x-intercepts, we must solve the equation:

x²+ 3x - 10 = 0

Factoring the equation, we get:

(x+5)(x-3)(x+1) = 0

The solutions of this equation are x = -5, -1, and 3. Therefore, the x-intercepts of the equation are -5, -1, and 3.

To find the y-intercept, we must plug 0 in for x in the equation:

y = x² + 3x - 10/ (x+1)(x-3)(x+5)

When x = 0, we get:

y = -10/ (0+1)(0-3)(0+5)

Therefore, the y-intercept of the equation is -10.

The vertical asymptote of the equation is the line x = -1, since it is the only value of x that makes the denominator equal to 0.

The horizontal asymptote of the equation is the line y = 0, since the degree of the numerator is less than the degree of the denominator.

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The y-intercept of the equation is -10.the x-intercepts of the equation are -5, -1, and 3.

Equation is a mathematical statement that expresses the equality of two expressions, which are separated by an equals sign. It can be used to represent a variety of different relationships, such as equality, inequality, addition, subtraction, multiplication, and division. Equations can be used to solve a variety of problems in science, engineering, and mathematics.

The x-intercepts of the graph of the equation r(x) are those values of x for which the equation is equal to 0. To find the x-intercepts, we must solve the equation:

x²+ 3x - 10 = 0

Factoring the equation, we get:

(x+5)(x-3)(x+1) = 0

The solutions of this equation are x = -5, -1, and 3. Therefore, the x-intercepts of the equation are -5, -1, and 3.

To find the y-intercept, we must plug 0 in for x in the equation:

y = x² + 3x - 10/ (x+1)(x-3)(x+5)

When x = 0, we get:

y = -10/ (0+1)(0-3)(0+5)

Therefore, the y-intercept of the equation is -10.

The vertical asymptote of the equation is the line x = -1, since it is the only value of x that makes the denominator equal to 0.

The horizontal asymptote of the equation is the line y = 0, since the degree of the numerator is less than the degree of the denominator.

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