Can the side lengths of 2 9 12 form a triangle yes or no can the side lengths of 3 5 8 form a triangle yes or no can the side lengths of 10 12 15 form a triangle yes or no can the side length of 4 4 7 form a triangle yes or no

Answer:

12 students didnt turn in a extra credit project at the end of the semester.

Step-by-step explanation:

Answer:

B

-10-10=20

10+10=20

20/20=0

Answer:

-2.4

Step-by-step explanation:

-54/22.5= -2.4

If it went down 54 degrees in 22.5 minutes, then you do -54/22.5, which gives you -2.4. So the temperature went down 2.4 F each minute. I think.

Answer:

The equation is 3/10 × s = 162

Alexandra's salary before taxes for the pay period was $540

Step-by-step explanation:

Let

Alexander's salary before taxes

=s

3/10 if Alexander's take home pay is $162 after taxes

3/10 of s = $162

The equation is

3/10 × s = 162

Divide both sides by 3/10

s = 162 ÷ 3/10

= 162 × 10/3

= 1620 / 3

= $540

Alexandra's salary before taxes for the pay period was $540

9514 1404 393

Answer:

Step-by-step explanation:

Just as the directions tell you, multiply both parts of the ratio by the same number. Here, the equivalents we used are 1, 2, and 5 times the numbers in the reduced ratio. Your multipliers can be anything, and don't need to be positive or rational or numbers.

__

1. 5/12 = (5·2)/(12·2) = 10/24

  5/12 = (5·5)/(12·5) = 25/60

__

2. 14:32 = (7·2):(16·2) = 7:16

  7:16 = (7·5):(16·5) = 35:80

__

3. 3 to 4 = (3·2) to (4·2) = 6 to 8

  3 to 4 = (3·5) to (4·5) = 15 to 20

__

4. 7/8 = (7·2)/(8·2) = 14/16

  7/8 = (7·5)/(8·5) = 35/40

  7/8 = (7·m)/(8·m) = (7m)/(8m) . . . m ≠ 0

If the password contains exactly 7 letters and letters cannot be used more than once, the number of possible passwords will be the number of ways to choose 7 letters out of the total 26 letters in the alphabet without repetition.

To find out the number of ways to choose 7 letters out of the total 26 letters in the alphabet, we will use the formula for combinations without repetition which is given as, C(n,r) = n! / (r!(n-r)!), where n is the total number of objects, r is the number of objects to be chosen from n and ! is the factorial.

Let's put the values, n = 26 and r = 7C(26,7) = 26! / (7!(26-7)!) = 26! / (7!19!) = (20*21*22*23*24*25*26) / (1*2*3*4*5*6*7)The above expression can be simplified as follows: (20*21*22*23*24*25*26) / (1*2*3*4*5*6*7) = 20*23*25*13 = 149500

Summary: There are 149500 possible passwords of 7 letters from a total of 26 letters if letters cannot be used more than once.

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Answer:

10%

Step-by-step explanation:

30+15=45

45 is 10% of 450 as 450/10= 45

Answer:

be a school leader as an adolescent

Step-by-step explanation:

Answer:

155,588

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = growth rate

N = number of years 2021 - 2014 = 7

130,000(1.026)^7 = 155,587.6

rounding off to the nearest whole  number is 155,588

To round off to the nearest whole number, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

Given:

The suns diameter is 10 times the diameter of Jupiter.

Jupiter is 11 times larger than earth.

To find:

How much larger than earth is the sun?

Solution:

Let the diameter of earth be x.

Jupiter is 11 times larger than earth. So,

Diameter of the Jupiter = 11x

The suns diameter is 10 times the diameter of Jupiter. So,

Diameter of sun = 10(11x)

Diameter of sun = 110x

Since, diameter of earth is x and diameter of sun is 110x, therefore, diameter of sun is 110 times of the earth.

Hence, the sun is 110 times larger than earth.

The diameter of the sun is 110 times greater than the diameter of the earth.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The sun's diameter is 10 times the diameter of Jupiter. If Jupiter is 11 times larger than earth.

Let the diameter of the Sun, Jupiter, and Earth be S, J, and E respectively

Then we have

S = 10J ...1

J = 11 E ...2

From equations 1 and 2, we have

S = 10 × 11 E

S = 110 E

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The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y ≤ - 5/6x + 2/3

Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.

Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.

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Answer:

the answer is-14 please do you get it

Answer:

Whats the question?

Step-by-step explanation:

We have a transformation for the triangle EFG. In this case is a translation.

We can verify with one of the points which one of the graphs correspond to this transformation.

The transformation is:

(x,y) --> (x-3, y + 1)

We look at point E = (-0.5, 0).

We apply the transformation and get:

(-0.5, 0) --> (-0.5-3, 0+1) = (-3.5, 1)

Then, the graph that has E located in the point (-3.5, 1) is the right one.

The A + 15d = 10, the value of d is -A when the 21st term is twice the 16th term, and the value of K is either 0 or 1 - 2A/d when ∑k=1ku∗ = 0.

(A) The sum of the first 31 terms of an arithmetic series is given as 310. Using the formula for the sum of an arithmetic series, which is Sn = (n/2)(2a + (n-1)d), we can set up the equation: 310 = (31/2)(2A + 30d). Simplifying this equation leads to 2A + 30d = 20. Rearranging the equation gives A + 15d = 10, which shows that A + 15d is equal to 10.

(B) When the 21st term is twice the 16th term, we can use the formula for the nth term of an arithmetic series, which is An = A + (n-1)d. Setting up the equation 2(A + 15d) = A + 15d + 5d, where the 21st term is 2(A + 15d) and the 16th term is A + 15d, we simplify it to 2A + 30d = A + 20d. By solving this equation, we find that d = -A.

(C) To find the value of K when ∑k=1ku∗ = 0, we need to determine when the sum of the first n terms of the series equals zero. Using the formula for the sum of the first n terms of an arithmetic series, which is Sn = (n/2)(2a + (n-1)d), we set up the equation (K/2)(2A + (K-1)d) = 0. Since the product of two factors is zero, either K/2 = 0 or 2A + (K-1)d = 0. From the first equation, K = 0. From the second equation, we can solve for K in terms of A and d, which gives K = 1 - 2A/d.

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The answer is yes, (x + 6) is a possible length of a rectangle with area x² + x − 30.

To determine whether (x + 6) is a possible length of a rectangle with area x^² + x − 30, we can use an area model to visualize the situation.

First, we need to find the width of the rectangle.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are given that the area is x² + x − 30, so we can set this equal to lw and solve for w:

x² + x − 30 = (x + 6)w

w = (x² + x − 30)/(x + 6)

The length of a rectangle must be greater than or equal to its width, so we need to check whether (x + 6) is greater than or equal to (x² + x − 30)/(x + 6). This simplifies to:

(x + 6) ≥ x² + x − 30

Expanding the left side and simplifying, we get:

x² + 12x + 36 ≥ x² + x − 30

11x ≥ -66

x ≥ -6

Since x must be a positive number (since we are dealing with lengths), we can conclude that (x + 6) is the possible length of the rectangle. Therefore, the answer is yes, (x + 6) is a possible length of a rectangle with an area x² + x − 30.

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Answer:

area ≈ 12.505

perimeter ≈  16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² =  the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

The odds she will win this competition is 14 to 11.

What is probability?

Odds in favor of an event is ratio of probability of an event to its completion:

Probability =0.56 / 1-0.56

= 0.56/0.44

= 56/44

= 14/11

Hence, the odds she will win this competition is 14 to 11.

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The area of the parallelogram formed by the given vertices A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), and D(0, 3, 2) is 2√21 square units.

To calculate the area of a parallelogram, we can use the cross product of two vectors formed by the sides of the parallelogram. The vectors AB and AD can be calculated by subtracting the coordinates of the initial and final points.

The cross product of these vectors gives us a vector representing the area of the parallelogram. Taking the magnitude of this vector gives us the area of the parallelogram. The magnitude of the cross product of AB and AD is 24, so the area of the parallelogram is 24 square units.

In this case, the vector AB is (-3, 7, 3), and the vector AD is (-1, 3, 3). Taking the cross product of these vectors gives us the vector (-12, 6, 24). The magnitude of this vector is √(12² + 6² + 24²) = √756 = 2√21. Therefore, the area of the parallelogram is 2√21 square units.

Complete Question:

Find the area of the parallelogram whose vertices are A(1, 0, −1), B(1, 7, 2), C(2, 4, −1), D(0, 3, 2).

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Answer:

-8

Step-by-step explanation:

+16-16=0

-(-24)+12-(+36)=0

So +16-(-24)+(-8)-16+(12)-(+36)=-8

Answer: -8

Step-by-step explanation:

Given expression

16 - (-24) + (-8) - 16 + (12) - (36)

Expand parentheses and change signs when [-] sign is in front

=16 + 24 - 8 - 16 + 12 - 36

Combine all the terms through addition/subtraction

=40 - 8 - 16 + 12 - 36

=32 - 16 + 12 - 36

=16 + 12 - 36

=28 - 36

=\(\boxed{-8}\)

Hope this helps!! :)

Please let em know if you have any questions

To find the critical numbers of the function provided , we need to determine the values of x at which the derivative of g(x) equals zero or does not exist.

First, let's find the derivative of g(x). Applying the product rule and chain rule, we have:

\(g'(x) = 8e^{(8x)cosh(10x) + e^(8x)(10sinh(10x))}\\ = e^{(8x)(8cosh(10x) + 10sinh(10x))\)

Now, to find the critical numbers, we set g'(x) equal to zero and solve for x:

\(e^{(8x)(8cosh(10x) + 10sinh(10x)) = 0\)

8cosh(10x) + 10sinh(10x) = 0

\(8((e^{(10x) + e^(-10x))/2) + 10((e^(10x) - e^(-10x))/2) = 0\)

on simplifying and combining like terms , will get:

\(9e^{(10x) }+ e^{(-10x) = 0\)

Dividing both sides by \(e^{(-10x)\), we obtain:

\(9e^{(20x)\) = -1

Taking the natural logarithm of both sides, we have:

ln(9) + 20x = ln(-1)

However, ln(-1) is undefined since the natural logarithm is only defined for positive values. Therefore, there are no critical numbers for the function g(x) = \(e^{8x)}cosh(10x).\)

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In a primitive Pythagorean triple, the sides a, b, and c are all integers, and they satisfy the equation a^2 + b^2 = c^2.

Now, let's assume that neither x nor y is divisible by 3. This means that x and y can only be 1, 2, 4, 5, 7, or 8 modulo 3. Therefore, x^2 and y^2 can only be 1 or 4 modulo 3. Now, let's consider the equation a^2 + b^2 = c^2 mod 3. If a and b are both 1 or both 2 modulo 3, then their squares will add up to 2 modulo 3, which is not a quadratic residue. Therefore, one of a and b must be 0 modulo 3, and hence, c must also be divisible by 3. We assumed that neither x nor y is divisible by 3. We then looked at the possible residues of x and y modulo 3 and saw that they can only be 1, 2, 4, 5, 7, or 8 modulo 3. We then used the fact that the sum of two quadratic residues is not a quadratic residue modulo 3, and concluded that one of a and b in the Pythagorean triple must be divisible by 3.

In conclusion, either x or y in a primitive Pythagorean triple must be divisible by 3. This is a result of the fact that the sum of two quadratic residues is not a quadratic residue modulo 3.

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Answer:

its A

Step-by-step explanation:

i did the test

Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer:

65º

Step-by-step explanation: