1.4 has 2 significant digits as a result of which rule? a. All nonzero numbers are significant. b. Zeros between nonzero digits are significant. c. Final zeros after the decimal point are significant. d. Zeros used solely for spacing the decimal point are not significant.

Answer:

15

Step-by-step explanation:

Divide the numbers:

122+3⋅6−9

6+3⋅6−9

Multiply the numbers

6+3⋅6−9

6+18−9

Add the numbers

6+18−9

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we are asked to determine the surface area of the figure. To do that we need to find the areas of each face and add them together. The front face is a trapezoid, and its area is:

Where "b" is the upper base, "B" is the lower base and "h" is the height. Replacing the values:

Solving the operations:

the upper face is a rectangle, its area is the product of its side:

The area of the lower face is also a rectangle, therefore its area is:

The side face is also a rectangle, and its area is:

Now we add the areas having into account that the front and side faces repeat themselves. the total surface area is:

replacing the values:

Solving the operations:

Therefore, the surface area is 286 square feet.

Answer:

24

Step-by-step explanation:

3(4)(2) (three times the variables)

12(2) (three times 4)

24 (twelve times 2)

\(\large\text{Hey there!}\\\\\\\large\textsf{3xz}\\\large\textsf{= 3(4)(2)}\\\large\textsf{= 12(2)}\\\large\textsf{= 24}\\\\\boxed{\large\text{Therefore, your answer is: \textsf{24}}}\huge\checkmark\\\\\large\text{Good luck on your assignment \& enjoy your day!}\\\\\frak{Amphitrite1040:)}\)

The man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).

To calculate the number of unique paths the man can take to travel from point (0,0) to point (50,51), we can use the concept of combinatorics.

The man needs to take a total of 50 steps horizontally (to reach the x-coordinate 50) and 51 steps vertically (to reach the y-coordinate 51). He can only move either to the right (horizontally) or upwards (vertically) at each step.

To reach the destination, the man needs to make a total of 50 + 51 = 101 steps.

Now, we need to determine in how many ways the man can arrange these 101 steps.

The number of unique paths can be calculated using the binomial coefficient formula, which is given by:

C(n, k) = n! / (k!(n-k)!),

where n represents the total number of steps and k represents the number of steps in one direction (either horizontally or vertically).

In this case, n = 101 (total steps) and k = 50 (number of steps in one direction).

Using the formula, we can calculate the number of unique paths as:

C(101, 50) = 101! / (50!(101-50)!) = (101! / 50!51!) = 101C50.

Calculating this combination:

C(101, 50) = 101C50 = 101! / (50!51!) ≈ 1.5820708e+30.

Therefore, the man has approximately 1.5820708e+30 unique paths to choose from to make the trip from (0,0) to (50,51).

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The coordinates of point T exists (0,5) and the midpoint of ST is (5,-2) then the coordinates of point T is S(10, -9).

Use midpoint formula and assume S(x, y):

(0 + x)/2 = 5

⇒ x / 2 = 5

⇒ x = 10

(5 + y)/2 = -2

⇒ 5 + y = -4

⇒ y = -4 - 5

⇒ y = -9

The complete question is:

The coordinates of point T are (0,5). The midpoint of ST is (5,-2). Find the coordinates of point S.​

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We need at least n = 127 terms to ensure the remainder is less than 0.0005 for infinite series.

We can use the formula for the remainder of a convergent geometric series:

R = a(1 - \(r^n\))/(1 - r)

where R is the remainder, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2/5, r = (1/5)² = 1/25, and we want R < 0.0005. Substituting these values and solving for n, we get:

0.0005 > (2/5)(1 - \((1/25)^n\))/(1 - 1/25)

0.0005(24/25) > 1 - \((1/25)^n\)

\((1/25)^n\) > 0.9992

n log(1/25) > log(0.9992)

n < log(0.9992)/log(1/25)

n > 126.06

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Answer:

1/2x plus -2

Step-by-step explanation:

Answer:

3.3.14259265359 re-uccering

Step-by-step explanation:

The first five terms of the sequences are

From the question, we have the following sequence notation that can be used in our computation:

aₙ = √(6n -5)

Set n = 1 to 5

So, we have

a₁ = √(6(1) -5) = 1

a₂ = √(6(2) -5) = √7

a₃ = √(6(3) -5) = √13

a₄ = √(6(4) -5) = √19

a₅ = √(6(5) -5) = 5

For the second sequence, we have

aₙ = (-6)ⁿ

a₁ = (-6)¹ = -6

a₂ = (-6)² = 36

a₃ = (-6)³ = -216

a₄ = (-6)⁴ = 1296

a₅ = (-6)⁵ = -7776

For the third sequence, we have

aₙ = (-6)ⁿ

a₁ = 4 + 2(-1)¹ = 2

a₂ = 4 + 2(-1)² = 6

a₃ = 4 + 2(-1)³ = 2

a₄ = 4 + 2(-1)⁴ = 6

a₅ = 4 + 2(-1)⁵ = 2

For the fourth sequence, we have

a₁ = 5, and aₙ = aₙ₋₁ + 1

a₁ = 5

a₂ = 5 + 1 = 6

a₃ = 6 + 1 = 7

a₄ = 7 + 1 = 8

a₅ = 8 + 1 = 9

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Question

If aₙ = √(6n -5), list the first five terms of an, starting with n = 1:

{a1, a2, a3, a4, a5} = [  ]

If aₙ = (-6)ⁿ, list the first five terms of an, starting with n = 1: {a1, a2, a3, a4, a5} = [  ]

If aₙ = 4 + 2(-1)ⁿ, list the first five terms of an, starting with n = 1: {a1, a2, a3, a4, a5} = [  ]

If a₁ = 5, and aₙ = aₙ₋₁ + 1, list the first five terms of an, starting with n = 1: {a1, a2, a3, a4, a5} = [  ]

Step-by-step explanation:

The formula for a parallelogram is A=Base x Height

So you multiply the base, which is 6, and the height, which is 4.

A=6x4

Hope it helps!

Answer:

I found this. Will this help??

Step-by-step explanation:

In the given triangle RSQ and ΔRST it is given that

∠RTS ≅ ∠SRQ ≅ 90°

∠RSQ is common in two triangles Δ RSQ and Δ RST.

Therefore two angles are equal so both the triangles are common.

From this property we opposite sides of the corresponding angles will be in the same ratio.

SR/SQ = ST/SR

x/(9 + 16) = 9/x

By cross multiplication on each side of the equation

x² = 25×9 = 225

x = √225 = 15

Therefore measurement of x is 15 units.

The value of x from the given right triangle is 20 units. Therefore, option C is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

From the given right triangle, we have ST = 9, TQ = 16 and RQ = x

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1) {∵ RT 丄 Hypotenuse SQ}

Δ SRQ ⩭ Δ RTQ ------(2) {∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

⇒ SR/ST = SQ/SR = RQ/TR

⇒ SR/9 = 25/SR = x/TR

⇒ SR² = 25 × 9

⇒ SR = 5 × 3 = 15

SR² + RQ² = SQ²

RQ² = SQ² - SR²

RQ² = 25² - 15²

RQ = x = √(625 - 225)

= √400

x = 20 units

Therefore, option C is the correct answer.

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Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2

a) The family should expect to sell the property for: $19,026.90.

b) The family should expect to sell the property for: $670,432.

The rate of change for each case is a percentage, hence exponential functions are used to model each situation.

For item a, the function has an initial value of 29000 and decays 10% a year, hence the value after x years is given as follows:

y = 29000(0.9)^x.

In the 4th year, the value is given as follows:

y = 29000 x (0.9)^4

y = $19,026.90.

For item b, the function has an initial value of 435500 and increases 4% a year, hence hence the value after x years is given as follows:

y = 435500(1.04)^x.

Then the value in 11 years is given as follows:

y = 435500(1.04)^11

y = $670,432.

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Answer:

-10 and -2/5

Step-by-step explanation

-10÷ \(-\frac{2}{5}\) = 25

Check

25 > 10

The 3rd term of the linear sequence above is 14.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 18 - 22

Common difference, d = -4

For the third term, we have:

a₃ =  a₁ + (n - 1)d

a₃ = 22 + (3 - 1)-4

a₃ = 22 - 8

a₃ = 14.

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Answer:

The simplified expression is equal to log(9).

Step-by-step explanation:

To condense the expression into a single logarithm, we can use the logarithmic identity that states that:

log(a*b) = log(a) + log(b)

First, we can simplify the expression inside the first set of parentheses:

2(log 18 - log 3) + 1/2 log 1/16

= 2log(18/3) + 1/2 log 1/16

= 2log(6) + 1/2 log 1/16

Next, we can simplify the expression inside the second set of parentheses using the logarithmic identity:

= 2log(6) + 1/2 log(1/16)

= 2log(6) + 1/2 log(1) - 1/2 log(16)

= 2*log(6) - 1/2 log(16)

Finally, we can use the logarithmic identity to condense the expression into a single logarithm:

= 2*log(6) - 1/2 log(16)

= log(6^2) - log(16^(1/2))

= log(36) - log(4)

= log(9)

Answer:

\(a {}^{2} + b {}^{2} = c {}^{2} \)

I hope this help

When the value of the variable x is greater than or equal to -3, the result returned by the even function is 3.

x=-1x=−1x, equals, minus, 1, Then the correct option is C.

A true function f(x) is an even function if the yield value of the function f(-x) is the same as the value returned by the function f(x) for all values of x that fall within the domain of f.

It is recommended that the equation be saved in an even function:

f(-x) = f(x)

Therefore

f(x) = f(3) = 3

Let's assume that f(x) is a function that always returns even. Then there is also

f(-3) = f(3) = 3

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CQ

Select all input values for which f(x)=3f(x)=3f, left parenthesis, x, right parenthesis, equals, 3.

Choose all answers that apply:

(Choice A)

A

x=-5x=−5x, equals, minus, 5

(Choice B)

B

x=-3x=−3x, equals, minus, 3

(Choice C)

C

x=-1x=−1x, equals, minus, 1

(Choice D)

D

None of the above

Teniendo en cuenta la definición de sistema de ecuaciones lineales, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

En este caso, se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.

Se sabe que el volumen de A es el doble del de B → A=2B

Las tres medidas llenan el depósito → A+ B +C= 24 L

Las dos primeras medidas llenan hasta la mitad del recipiente → A +B= 24 L÷2 → A +B= 12 L

Entonces, el sistema de ecuaciones a resolver es el formado por las tres ecuaciones anteriormente mencionadas.

Existiendo diversos métodos para resolver un sistema de ecuaciones, se decide resolver mediante el método de sustitución, que consiste en despejar una de las dos variables en una de las ecuaciones del sistema y sustituir su valor en la otra ecuación.

En este caso, reemplazando la primer ecuación en la tercera ecuación se obtiene:

2B +B= 12 L

3B= 12 L

B= 12 L÷3

B= 4 L

Reemplazando este valor en la primer ecuación se obtiene:

A=2B

A=2×4 L

A= 8 L

Finalmente, para obtener el valor de C se reemplaza el valor de A y B en la segunda ecuación:

A + B + C= 24 L

8 L + 4 L + C= 24 L

12 L + C= 24 L

C= 24 L - 12 L

C= 12 L

Finalmente, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

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Answer:, Volume of triangular prism = (1/2) bh × L.

The Elimination equations: 3s = 33, s = 11.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

5s+3t=30

-1(2s+3t=-3)

which will eventually

5s+3t=30

-2s-3t=3

which then becomes

3s = 33, s=11

Hence, The Elimination equations: 3s = 33, s = 11.

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Hence, 1) 6 cm (smallest value), 2) 6 cm, and 3)15.167 cm are the approximate dimensions which will result in a material with the biggest volume (largest value).

A 3D object's surface area is indeed the entire area that all of its faces cover. For instance, the surface area of a cube has been its surface area if we need to determine how much paint is needed to paint it. It's always calculated in square units.

Let the height be y as well as the side length of a square base be x. The rectangular solid's surface area is then determined by:

When we simplify this equation, we obtain:

The rectangular solid's volume is determined by:

V = x² × y = x² × (433.5 - 4x²) / (2x)

When we simplify this equation, we obtain:

V = 216.75x - 2x³

We must determine the value of x that maximizes V in order to determine the dimensions that lead to a solid with the maximum volume. Using V's derivative with x as the base, we can calculate:

dV/dx = 216.75 - 6x²

By setting this to 0 and figuring out x, we obtain:

216.75 - 6x² = 0

x² = 36.125

x ≈ 6.005

When we rewrite the equation for y using this value of x, we obtain:

y ≈ 15.167

Thus, the following dimensions will produce a solid with the largest volume:

1. 6 cm (smallest value)

2. 6 cm

3.15.167 cm (largest value)

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The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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Let's redraw the traingle

if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ∆CBD ~ ∆ABC, ∆ACD ~ ∆ABC, and ∆CBD ~ ∆ACD.

This means that

Replacing

Answer:

16

Step-by-step explanation:

Using PEMDAS:

3 + 9 x 2 - 5

= 3 + 18 - 5

= 21 - 5

= 16

9514 1404 393

Answer:

  f(x) = (x -6)(x +2)

Step-by-step explanation:

The graph shows the x-intercepts are -2 and +6. The factors will be binomials such that these values make the factors zero: (x +2) and (x -6).

  f(x) = (x -6)(x +2)

Answer:

1.08 = m

Step-by-step explanation:

2= 2.27- m/4

Subtract 2.27 from each side

2-2.27= 2.27-2.27- m/4

-.27 = -m/4

Multiply each side by -4

-.27 * -4 = -m/4 *-4

1.08 = m