The first term of an arithmetic sequence is six. The fifth term of the sequence is -14. th Write a rule that can be used to find the nth term.​

Answer:

Step-by-step explanation:

Answer: x=5

Good luck :)

Answer:

? = 7.45

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side/ hypotenuse

cos 20 = 7 / ?

Multiply each side by ?

? cos 20 = 7

Divide each side by cos 20

? = 7/ cos 20

? =7.449244407

To the nearest hundredth

? = 7.45

Answer:

7.45 units

Step-by-step explanation:

\(\cos 20\degree = \frac{BC}{AB}\\\\0.939692620 = \frac{7}{AB}\\\\AB = \frac{7}{0.939692620}\\AB = 7.4492\\AB = 7.45 units\)

Answer:

I would use quaro is is faster.

Step-by-step explanation:

The Lateral Area and Total Area of the given shapes are:

2)
LA = 2040cm²

TA = 6360cm².

3)
LA = 324m

TA = 351m

4)
LA = 1000cm²

TA =  3232cm²

5)

LA = 124.71 cm²

TA = 155.90 cm²

2) The lateral area of a cuboid is the combined surface area of all the sides of the cuboid excluding the top and bottom faces.

The total surface area of a cuboid is the sum of the lateral area and the area of the top and bottom faces.

To calculate the lateral area of the given cuboid, we need to add the areas of the four lateral faces:

Lateral Area = 2 x Length x Height + 2 x Breadth x Height

Lateral Area = 2 x 38cm x 15cm + 2 x 30cm x 15cm

Lateral Area = 1140cm² + 900cm²

Lateral Area = 2040cm²

To calculate the total surface area of the cuboid, we need to add the area of the top and bottom faces as well:

Total Area = Lateral Area + 2 x Length x Breadth + 2 x Length x Height + 2 x Breadth x Height

Total Area = 2040cm² + 2 x 38cm x 30cm + 2 x 38cm x 15cm + 2 x 30cm x 15cm

Total Area = 2040cm² + 2280cm² + 1140cm² + 900cm²

Total Area = 6360cm²

Therefore, the lateral area of the given cuboid is 2040cm², and the total surface area of the cuboid is 6360cm².


3)

LA = P (L*W)

= (Side 1 + Side 2 + Side 3) (L*W)

= (4m+ 3m + 5m) (9*3)

LA = 324m

TA = P(L*W) + 2(L*W)

TA = (11 (27)) + 2(27)
TA = 321m

4)

The lateral area of a cuboid is the combined surface area of all the sides of the cuboid excluding the top and bottom faces.

The total surface area of a cuboid is the sum of the lateral area and the area of the top and bottom faces.

To calculate the lateral area of the given cuboid, we need to add the areas of the four lateral faces:

Lateral Area = 2 x Length x Height + 2 x Breadth x Height

Lateral Area = 2 x 28cm x 10cm + 2 x 22cm x 10cm

Lateral Area = 560cm² + 440cm²

Lateral Area = 1000cm²

To calculate the total surface area of the cuboid, we need to add the area of the top and bottom faces as well:

Total Area = Lateral Area + 2 x Length x Breadth + 2 x Length x Height + 2 x Breadth x Height

Total Area = 1000cm² + 2 x 28cm x 22cm + 2 x 28cm x 10cm + 2 x 22cm x 10cm

Total Area = 1000cm² + 1232cm² + 560cm² + 440cm²

Total Area = 3232cm²

Therefore, the lateral area of the given cuboid is 1000cm², and the total surface area of the cuboid is 3232cm².


5)
To find the lateral area, we need to find the area of all the rectangular faces and add them together. The area of each rectangular face is:

Area = length x height = 6 cm x (4√3 cm) = 24√3 cm².

Area ≈ 41.57 cm².

There are three rectangular faces, so the total lateral area is:

Lateral area = 3 x 41.57 cm². ≈ 124.71 cm²

To find the total area, we need to add the area of the two equilateral triangles to the lateral area. The area of each equilateral triangle is:

Area = (√3 / 4) x base² = (√3 / 4) x 6² = 9√3 cm²

Area ≈ 15.59 cm²

There are two equilateral triangles, so the total area of both triangles is:

Total area of both triangles = 2 x 15.59 cm² ≈ 31.19 cm².

Therefore, the total area of the prism is:

Total area = lateral area + total area of both triangles

Total area ≈ 124.71 cm² + 31.19 cm² ≈ 155.90 cm²

So, the lateral area of the prism is approximately 124.71 cm² and the total area is approximately 155.90 cm²

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Notice that the intersection between both functions on the positive values of x is near the line x=2. From the provided options, the closest to that value is 1.7

Then, the positive solution to f(x)=g(x) is closest to:

The value of the velocity, u is 19.6 m/s.

The greatest height reached by the particle is 19.6 m.

The total time during which the particle is at a height greater than half its greatest height is 2.33 s.

a) To find the value of the velocity, u, we can use the formula for the time of flight of a vertically projected particle:

t = 2u/g

Since the particle returns to the same point after 4 seconds, we have:

2t = 4

Substituting the value of t in the first equation, we get:

u = gt/2 = 9.8 x 2

u = 19.6 m/s

b) To find the greatest height reached by the particle, we can use the formula for the maximum height reached by a vertically projected particle:

h = u^2/2g

Substituting the value of u, we get:

h = 19.6^2/(2 x 9.8)

h = 19.6 m

c) To find the total time during which the particle is at a height greater than half its greatest height, we can first find the height at which the particle is at half its greatest height:

h/2 = (u^2/2g)/2 = u^2/4g

Substituting the value of u, we get:

h/2 = 19.6^2/(4 x 9.8) = 24.01 m

So, the particle is at a height greater than half its greatest height when it is above 24.01 m.

Next, we can find the time taken by the particle to reach this height:

h = ut - (1/2)gt^2

24.01 = 19.6t - (1/2)9.8t^2

Solving this quadratic equation, we get:

t = 2.33 s or t = 4.10 s

The particle takes 2.33 s to reach a height of 24.01 m, and it takes another 1.67 s (4 - 2.33) to return to the ground.

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The percentage of operations that succeed and are free from infection is 86%.

To determine the percentage of operations that succeed and are free from infection, we need to subtract the probabilities of infection and failure from 100%.

Infection occurs in 4% of the operations.

The repair fails in 12% of the operations.

Both infection and failure occur together in 2% of the operations.

Let's calculate the percentage of operations that succeed and are free from infection:

Percentage of operations with infection = 4%

Percentage of operations with failure = 12%

Percentage of operations with both infection and failure = 2%

Percentage of operations without infection = 100% - 4% = 96%

Percentage of operations without failure = 100% - 12% = 88%

Percentage of operations without infection and failure = 100% - (4% + 12% - 2%) = 86%

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Step-by-step explanation:

s for small stones

l for large

4s+6l<=30 (<= means less or equal to because I couldn't get the sign on here).

s+l>=4. (>= means greater than or equal to).

Possible Answers:

s+l=5 (if she bought 5 stones in total)

answer #1: 5 large stones and 0 small stones.

s+l=6 (if she bought 6 stones in total)

answer #2: 3 large stones and 3 small stones.

so sorry i couldn't do the graphing part...

The two possible solutions are; x = 5, y = 0 and x = 5, y = 1

Linear inequalities are defined as a mathematical expression in which two expressions are compared using the inequality symbol.

Given that, Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The gift shop sells small stones for $4 and large stones for $6. Emily has $30 to spend.

Let the number of $4 and $6 stones that Emily can buy be x and y respectively.

According to question,

Since, Emily wants to gift to at least 4 friends, so,

x + y ≥ 4 ............ (i)

Also, she can spend a maximum of $30 only,

4x + 6y ≤ 30 ............... (ii)

Studying graph we get solutions;

x = 5, y = 0

and x = 5, y = 1

Hence, The two possible solutions are; x = 5, y = 0 and x = 5, y = 1

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1. Correct option D. y= 4/5x-9/5

2. option C. (4, 0) is a solution.

3. option B, is the correct answer.

4. option B. (11, 1), is a solution.

5. option A, "(1,7) and (7,1)" is a correct answer.

A statement proving the equality of two mathematical expressions is known as an equation.

1. Solve the equation for y:  4x - 5y = 9  

⇒ 5y = 4x - 9

⇒ y = 4/5 x - 9/5  (correct option D)

2. Solution of this equation:  7a - 5b = 28

from the given options we simply substitute the values of a and b into the equation and check if the equation holds true.

option C. (4, 0);

Substituting a=4 and b=0 into the equation 7a-5b=28, we get:

7(4) - 5(0) = 28, which is equal to 28. So (4, 0) is a solution.

3. we simply substitute the values of x and y into the equation and check if the equation holds true.

Substituting x=2 and y=-9 into the equation 5x-y/3=13, we get:

5(2) - (-9)/3 = 10 + 3 = 13, which is equal to 13. So (2,-9) is a solution.

Substituting x=3 and y=-6 into the equation 5x-y/3=13, we get:

5(3) - (-6)/3 = 15 + 2 = 17, which is not equal to 13. So (3,-6) is not a solution.

Therefore, option B, "The first is a solution, but the second is not" is the correct answer.

4. we simply substitute the values of x and y into the equation and check if the equation holds true.

option B. (11, 1), Substituting x=11 and y=1 into the equation (x+3)y=14, we get: (11+3)(1) = 14(1) = 14, which is equal to 14. So (11,1) is a solution.

5. we substitute each pair into the equation and check if it holds true.

option A. (1,7) and (7,1); Substituting x=1 and y=7 into the equation 4xy+8=36, we get: 4(1)(7) + 8 = 28 + 8 = 36, which is equal to 36. So (1,7) is a solution.

Substituting x=7 and y=1 into the equation 4xy+8=36, we get:

4(7)(1) + 8 = 28 + 8 = 36, which is equal to 36. So (7,1) is also a solution.

Therefore, option A, "(1,7) and (7,1)" is a correct answer.

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The answers of the given equations are

1. option D

2.option C

3. option B

4.option B

5.option A.

What is equation?

Equation is basically a mathematical statement where two expressions are connected by a equal sign. It contains atleast one variable that has be determined.

1) Given equation is 4x- 5y= 9

To solve this equation at first we subtract 4x from both sides

                         -5y= 9-4x

Multiplying by '-' sign to the both sides of the equation we get,

                         5y= 4x-9

Dividing by 5 on the both sides of equation we get,

                      y= (4/5)x - (9/5)

Hence option D is correct.

2) Given equation is 7a-5b = 28----------(1)

putting a=4 and b=0  in equation (1) we get,

                  7× 4- 5×0=28

Hence the ordered pair ( 4,0) is the solution of the equation as the value of a and b satisfies the right side of equation (1). option C.

3) Given equation is 5x- y/3= 13-----------(2)

Putting (2,-9) in equation (2) we get,

  10+3=13 which is the RHS of equation (2)

Putting (3,-6) in equation (2) we get,

  15+2=17 which is not the RHS of equation (2)

So the first is a solution of the equation but the second is not.

Option B.

4) Given equation is (x+3)y=14---------(3)

Putting the values (11,1) in equation (3) we get,

(11+3)×1= 14 which is the RHS of the equation (3).

So the ordered pair is (11,1).

Option B.

5) Given equation is 4xy+8=36

It can be deduced to,

                      4xy+8=36

                       4xy= 36-8

                        4xy= 28

                           x y= 7-------(4)

Putting (1,7) and (7,1) in equation (4) we get,

                      1×7=7×1=7 which is the RHS of equation (4)

So the pair is (1,7) and (7,1). Option A.

Hence, the answers are

1. option D

2.option C

3. option B

4.option B

5.option A.

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Step-by-step explanation:

15,910 like what said of calculator

Answer:

[4]x+[8]=[1×]+2

Step-by-step explanation:

x will be negative now that the more x you have the higher your number will have to be.

The requried, x is negative, the left-hand side of the equation is positive, but the right-hand side is negative, so the equation has a negative solution as x = -3.5.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
One possible solution is,

[1]x + [2] = [3]x + [9]

To see that this equation has a negative solution, we can rearrange it to get:

x + 2 = 3x + 9

x - 3x = 9 - 2
-2x = 7
x = -3.5

Since x is negative, the left-hand side of the equation is positive, but the right-hand side is negative, so the equation has a negative solution.

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ITS 67 dgrees Step-by-step explanation: NP BRAINLIEST OR NA :)?

The angle that you would have to look up to see the peak if you were standing at the edge of the ocean is 18.4°.

Let x represent the angle

Tan x=Height/Horizontal distance

Tan x =10,000/30,000

x=Tan^-1 (1/3)

x=18.4°

Inconclusion the angle that you would have to look up to see the peak if you were standing at the edge of the ocean is 18.4°.

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The formula connecting E and F is E = k/F3, where k is a constant. This formula states that the value of E is inversely proportional to the cube of F.

That is, as F increases, the value of E decreases. For example, if F increases from 3 to 4, then the value of E decreases by a factor of 8.

This inverse proportionality between E and F3 is due to the fact that, as F increases, the cube of F increases at a faster rate. In other words, when F doubles, the cube of F increases by a factor of 8. This causes the value of E to decrease by the same factor of 8.

The formula is useful in many applications, such as in physics and engineering. For example, in physics, the formula can be used to calculate the force of an object in a gravitational field. The force is inversely proportional to the cube of the distance between the object and the center of gravity, where the constant k is equal to the gravitational constant. In engineering, the formula can be used to calculate the power of a motor, where the power is inversely proportional to the cube of the speed of the motor.

Overall, the formula E = k/F3 expresses the inverse proportionality between E and F3, and is used in various applications to calculate the value of E given the value of F.

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Answer:

No i does not well it will be 0,5 or any other number but the x wont change

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

By answering the presented question, we may conclude that Therefore, domain (f+g)(-2) = 17 and (f-g)(-2) = 31.

The domain of a function is the range of possible values that it can accept. These numbers represent the x-values of a function such as f. (x). The domain of a function is the range of possible values that can be used with it. This set includes the value returned by the method after adding the x value. A function with y as the dependant variable and x as the independent variable has the formula y = f. (x). When a single value of y can be created successfully from a value of x, that value of x is said to be in the function's domain.

To find (f+g)(x) and (f-g)(x), we need to add and subtract the two functions, respectively, and evaluate the resulting expressions at x.

\((f+g)(x) = f(x) + g(x) = (x^2 - 6x + 8) + (x - 5) = x^2 - 5x + 3\\(f-g)(x) = f(x) - g(x) = (x^2 - 6x + 8) - (x - 5) = x^2 - 7x + 13\\(f+g)(-2) = (-2)^2 - 5(-2) + 3 = 4 + 10 + 3 = 17\\(f-g)(-2) = (-2)^2 - 7(-2) + 13 = 4 + 14 + 13 = 31\\\)

Therefore, (f+g)(-2) = 17 and (f-g)(-2) = 31.

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Answer:

AC is 6.5 cm

Step-by-step explanation:

From trigonometric ratios:

\( \sin( \theta) = \frac{opposite}{hypotenuse} \\ \)

opposite » 3 cm

hypotenuse » AC

angle » 28°

\( \sin(28 \degree) = \frac{3}{AC} \\ \\ AC = \frac{3}{ \sin(28 \degree) } \\ \\ AC = \frac{3}{0.46} \\ \\ AC = 6.5 \: cm\)

Answer:

Here sin28 = perpendicular/hypotenuse

AC = sin28 * 3

AC = 0.46*3

AC = 1.38

The statement ''f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm '' is TRUE.

Let us assume that a is an m x n matrix that doesn't span rm. It means that the columns of a matrix don't contain all the vectors in the m-dimensional vector space that a is associated with. Therefore, it is not possible to find the linear combination of the columns of a that produces some vectors in rm.

We can also say that a matrix is inconsistent when there is no solution possible for the given linear equation. A system of linear equations is inconsistent when it has no solution.To prove the statement f, we need to prove that if a matrix doesn't span rm, then the given equation ax = b is inconsistent for some b in rm.

Here is a proof:

Let's assume that the columns of the matrix a don't span rm. It means that some vector in rm is not in the column space of a matrix.

Let's assume that vector is v.

Now, let's consider the linear equation ax = v. Since v is not in the column space of matrix a, there is no solution to this equation. It means that the equation ax = v is inconsistent.

Hence, we can say that the statement f. if a is an m n matrix whose columns do not span rm, then the equation ax d b is inconsistent for some b in rm is true

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Answer:

you dont need to round

Step-by-step explanation:

multiply v and U and then add the other numbers and that should work

Answer:

\(\huge\boxed{\sf r = 37\ mm}\)

Step-by-step explanation:

Let the radius be r

UV is tangent to the circle T which means UV is perpendicular to UT, that makes ΔUVT a right-angled triangle.

Which means:

∠TUV = 90°

So, We can use pythagoras theorem to find the radius of the circle.

In the Δ:

Hypotenuse = r + 9

Base = r

Perpendicular = 12

Pythagoras Theorem:

(Hypotenuse)² = (Base)² + (Perpendicular)²

(6 + r)² = (r)² + (22)²

(6)² + 2(6)(r) + (r)² = r² + 484

36 + 12r + r² = r² + 484

Subtract r² to both sides

36 + 12r = 484

Subtract 36 to both sides

12r = 484 - 36

12r = 448

Divide both sides by 12

r = 448/12

r = 37 mm

\(\rule[225]{225}{2}\)

0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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Answer:

174 m/s

Step-by-step explanation:

Formula: velocity = frequency x wavelength

V = 2 x 87

V = 174

Hope that helps!

Answer:

174

Step-by-step explanation:

Did the test

The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.

Toothpaste company

Large tubes

Small tubes

1) Sparkling

100 per hour

200 per hour

2) Bright White

100 per hour

250 per hour

3) Fresh!

200 per hour

250 per hour

4) Mint

150 per hour

150 per hour

Formula for comparative advantage is

CA=rate of producing large tubes/rate of producing small tube

For 1 Sparkling:

CA = 100/200

CA = 0.5

For 2 Bright White:

CA = 100/250

CA = 0.5

For 3 Fresh:

CA = 200/250

CA = 0.8

For 4 Mint:

CA = 150/150

CA = 1

thus, to place the companies in order of greatest comparative advantage to least comparative advantage in  producing large tubes of toothpaste is 4, 3, 1, 2.

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Complete question:

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in

producing large tubes of toothpaste.

2.1.3.4

4.1,2,3

4,3,1,2

Save and Exit

Next

Submit

Mark this and retum

Answer:

slope = - 2, y- intercept = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x , that is

y = - 2x + 0 ← is in slope- intercept form

with slope m = - 2 and y- intercept c = 0 ( that is the origin )

Answer:

the first i believe but the one with 50 confuses me

Step-by-step explanation:

Since ab > 0, it is clear that the discriminant D > 0. Therefore, the equation ax^2 + bx + c = 0 has two distinct real roots.

Since 4a + 2b + c = 0, we can rewrite c as c = -4a - 2b. Substituting this into the quadratic equation ax^2 + bx + c = 0 gives ax^2 + bx - 4a - 2b = 0. Factoring out an 'a' gives a(x^2 + (b/a)x - 4) - 2b = 0.

Since ab > 0, we know that a and b must have the same sign. This means that either both a and b are positive or both a and b are negative. In either case, (b/a) is negative. So we can rewrite the equation as a(x^2 - |(b/a)|x - 4) - 2b = 0.

To solve for the roots of the equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the coefficients, we get x = (-b ± √(b^2 - 4a(-4a-2b))) / 2a, which simplifies to x = (-b ± √(b^2 + 16ab)) / 2a.

Since ab > 0, we know that b^2 + 16ab > 0. Therefore, the quadratic equation ax^2 + bx + c = 0 has two real roots.

Based on the information provided, let's consider the equation ax^2 + bx + c = 0, where a, b, and c are real numbers and 4a + 2b + c = 0. Since ab > 0, both a and b have the same sign (either both positive or both negative).

The given equation can be rewritten as a quadratic equation in the standard form:

ax^2 + bx + c = 0

Using the discriminant formula, D = b^2 - 4ac, we can analyze the nature of the roots of the quadratic equation. Given that 4a + 2b + c = 0, we can express c as:

c = -4a - 2b

Now, let's plug this value of c into the discriminant formula:

D = b^2 - 4a(-4a - 2b)

D = b^2 + 16a^2 + 8ab

Since ab > 0, it is clear that the discriminant D > 0. Therefore, the equation ax^2 + bx + c = 0 has two distinct real roots.

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Answer:

relative

Step-by-step explanation:

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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Answer:

x = 3

Step-by-step explanation:

12x = 36

simply 12 will go to the other side and switches to the opposite sign for example + will be -

× will br ÷

so 36 ÷ 12 =3

x = 3