Which expressions are equivalent to z +(2+6)?
Choose all answers that apply:
(z + ) + (z +6)
(z +6 +6
212 +3)

The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }

Given data ,

Let the geometric sequence be represented as A

Now , the value of A is

A = 12 ( -2/5 )ⁿ

On simplifying , we get

when n = 1

A₁ = 12 ( -2/5 ) = -4.8

A₂ = 12 ( -2/5 )²

A₂ = 12 ( 4/25 ) = 1.92

A₃ = 12 ( -2/5 )³

A₃ = -12 ( 8/125 ) = -0.768

A₄ = 12 ( -2/5 )⁴

A₄ = 12 ( 16 / 625 ) = 0.3072

A₅ = 12 ( -2/5 )⁵

A₅ = -12 ( 32 / 3,125 ) = -0.12288

Hence , the geometric sequence is solved

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Figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

If a figure is the scale copy of another figure, the corresponding side lengths of both figures would be proportional to each other, which means their ratios would be the same.

From the figure given, the ratios of their side lengths are:

18/9 = 2

12/12 = 1

30/15 = 2

This shows that their ratios are not the same.

Therefore, we can conclude that figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

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The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:

x = -3 or x = 9.

The equation in Step 6 is given as follows:

\(\sqrt{(x - 3)^2} = \sqrt{36}\)

Simplifying the square roots, the variable x can be isolated, as follows:

Both -6 and 6 are correct results for the square root of 36, because:

His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:

From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;

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Answer:

x = -6, y = 27

Step-by-step explanation:

For the top equation;

\( \frac{x + y}{2} - \frac{x - y}{6} = 16\)

\(3(x + y) - (x - y) = 96\)

\(3x + 3y - x - y = 96\)

\(2x + 4y = 96\)

\(x + 2y = 48\)

For the bottom equation:

\( \frac{x}{3} + \frac{x + 2y}{3} = 14\)

\(x + x + 2y = 42\)

\(2x + 2y = 42\)

\(x + y = 21\)

Eliminating x by subtracting the two resulting equations, we have y = 27, and it follows that x = -6.

The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.

In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.

Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.

In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A

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A and B are Vertical Angles and are thus congruent.

A = B
3y - 24 = 51
3y - 24 + 24 = 51 + 24
3y = 75
3y/3 = 75/3
y = 25

We can solve for A, but we already know A = B and B = 51, so A = 51.

C and D are also Vertical Angles. Since these angles go all the way around, they add up to 360.

51 + 51 + C + D = 360
C = D
C = x
D = x
D + C = 2x
102 + 2x = 360
102 - 102 + 2x = 360 - 102
2x = 258
2x/2 = 258/2
x = 129

C = 129
D = 129

Answer:

=8x−2

Step-by-step explanation:

I hope this helps you

Answer:

-3 1/4 is the answer for this question

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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we can conclude that 2/3 is not equal to 4/5.

To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.

To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

For 2/3 and 4/5, we have:

2 * 5 = 10

3 * 4 = 12

Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.

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Answer:

Now first we have to found the decrease length.

which is:4mm-3mm=1mm

Now

we have to use formula to calculate the percentage which is

= decrease length/total length ×100%

=. 1/4×100%

=. 25 %

Therefore,the decrease rate is 25%.

Answer:

The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.

Step-by-step explanation:

Suppose we have a function y = f(x). The zeros, which are the values of x for which y = 0, are also called the x-intercepts of the function.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

I will write the function as a function of x, just exchanging a for x.

\(f(x) = x^{2} + 5x + 6\)

\(\bigtriangleup = 5^{2} - 4*1*6 = 1\)

\(x_{1} = \frac{-5 + \sqrt{1}}{2*1} = -2\)

\(x_{2} = \frac{-5 - \sqrt{1}}{2*1} = -3\)

The x-intercepts, or zeros, which are the values of x(or a in this problem) for which the function is 0, are x = a = -2 and x = a = -3.

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Geometric progression is given by:

\(nth\ term=ar^{n-1}\)

where a is the first term, r is the common ratio

Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3

\(First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486\)

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

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The answer I is -6. 3x6 is 18 and 18-24 is -6. So the answer is negative 6

Awnser : 6

Step-by-step explanation:

3×6=18

24-18=6

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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Answer:

33

Last answer: 28

sorry I didn't read it properly

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

18 + 10 sorry this is wrong its 33 my bad

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:28

Step-by-step explanation:

Trick: just check if it's divisible by both numbers

The sequence of steps that translates figure W to figure X are -

Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -

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Answer:

let width=x

length = x + 2ft

Area = 82ft^2

Area= length×width

=(x+2)x

=x^2 +2x=82

x^2+2x-82=0

Use Quadratic Equation to get x.

x = -10.1(reject, length cannot be minus value or 8.11)

x = 8.11

width = 8.11ft

length = 10.11ft

Answer:

Second option) Right 7 and down 4

Step-by-step explanation:

We will need to find the change that happened to solve:

(5, 1) - (-2, 5)

(7, -4)

[] This correlates with the second option (currently highlighted yellow) because the x-coordinate, which is left/right, is positive 7 and the y-coordinate, which is up/down, is negative 4. This means it'll move right 7 units and down 4 units, answering your question.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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