greater than, less than or equal. 5 1/7 ___ 4 3/4

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

11 4/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Vẽ góc vuông. - Trên hai canh góc vuô dùng thước thước có chia khoảng vẽ hai đoạn thẳng bằng nhau có chung một điểm và nối hai điểm còn lại.

Answer:210

Step-by-step explanation:2+1+0=210 ✨

Way: W = k * w  * h^2/ L

4 tons is maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long

Gravitational force of attraction on an object, caused by the presence of a massive second object, such as the Earth or Moon.

Given,

Maximum weight that a certain type of rectangular beam can support varies inversely as it’s length and jointly as its width and the square of its height.

beam 5 inches wide, 2 inches high and 10 feet long can support a maximum weight of 8 tons.

W = k × w × h²/ L

8 = k × 5 × 2² / 10

8 = k ×20/10

8 = 2 × k

k = 4

The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long

w =4 ×6 ×2² / 24

= 24 ×4/ 24

W=4 tons

Hence 4 tons is maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long

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Answer:

The answer is b

Step-by-step explanation:

As no table mentioned it can't be told which city accurately but you can find it by below precedence.

Find the city having temperature 10°F , that's the answer

Answer:

a

Step-by-step explanation:

Answer:

6x + 14y + 13

Step-by-step explanation:

combine the like terms.

(5+8), (2y + 12y), and 6x which will be dealt with after solving.

13 + 14y + 6x. And that is it because there are no more like terms to be put together.

Answer:

30mg

Step-by-step explanation:

10 mg/mL x 3 mL

Answer:

least common denominator of the rational expressions below is x(x-7)(x+3)

Step-by-step explanation:

factotized form of denominators

x²-7x

=x(x-7)

x²-4x-21

=x²-7x+3x-21

=x(x-7)+3(x-7)

=(x+3)(x-7)

i hope this will help you :)

Answer:

least common denominator of the rational expressions below is x(x-7)(x+3)

Step-by-step explanation:

factotized form of denominators

x²-7x

=x(x-7)

x²-4x-21

=x²-7x+3x-21

=x(x-7)+3(x-7)

=(x+3)(x-7)

i hope this will help you :)

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.

The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.

Given:

5√27 - 17√3

Simplify the value under roots,

5√(3 × 3 × 3) - 17√3

5 × 3 √3 - 17√3

√3 (15 - 17)

-2 √3

Therefore, the combination of radical 5√27 - 17√3 is -2 √3.

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The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

-17/8

Step-by-step explanation:

8-(-9)=17

-2-6=-8

17/-8

Answer: 3×4=12

Step-by-step explanation:

Brackets: X=1 , so 1+3=4 and 3+4=12

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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The value of the missing data point is 10. Option C

The data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.

Let's arrange the data set in ascending order:

6, 8, ?, 8, 14, 15, 16, 18

Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.

From the given options, the only whole number that could fit as the fourth value in the data set is 10.

Thus, the value of the missing data point is C. 10.

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Answer:

(7j + 1/8q + 3) - (5/8q - 11 + 2j)

7j + 1/8q + 3 - 5/8q + 11 - 2j

5j - 1/2q + 14

Answer:

100

Step-by-step explanation:

10(-2.5) = -25 since negative times positive is negative.

-25(-4)=100 since negative times negative is positive.

Basically, the negative inverts the sign so a negative negates a positive yielding a negative while a negative negates a negative yielding a positive.

Think of it as not not vs not

Answer:

166 2/3 meters/sec.

Step-by-step explanation:

1/1 =1  12 inches/1 foot =1  you are looking for equivalents that will cancel out the unit until you can get to meters and seconds.  See work in the picture.

Answer:

23.5

Step-by-step explanation:

12.3 + 17.8 - ( 3.3 x 2 )

12.3 + 17.8 - ( 6.6 )

30.1 - 6.6

23.5

Answer:

0.078 kg

Step-by-step explanation:

The conversion from grams to kilograms involves a division by a factor of 1000 as shown below:

78 / 1000 = 0.078

Therefore the sculpture weights 0.078 kg

Given:

We know that:

So the peak voltage can be calculated using the maximum value of the sine function (1 in this case). Then:

Answer:

The second amount is 3.72

Step-by-step explanation:

Given

\(First : Second = 8 : 3\)

\(First = 9.92\)

Required

Find Second

\(First : Second = 8 : 3\)

Substitute 9.92 for First

\(9.92: Second = 8 : 3\)

Express as fraction

\(\frac{Second}{9.92} = \frac{3}{8}\)

Multiply both sides by 9.92

\(9.92 * \frac{Second}{9.92} = \frac{3}{8}*9.92\)

\(Second = \frac{3}{8}*9.92\)

\(Second = 3.72\)

Answer:

the answer is attached herewith

ps.hv a great day ahead! :)

According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.

To illustrate this value on an abacus we must find the number of this operation as shown below:

Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:

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It is a better deal for Ella to use the loyalty card, since that way she will end up saving $0.29 for she would not have to pay for the sixth soda.

Using the loyalty card at the local store, Ella would get one soda for free after buying 5 sodas at the regular price of $0.89 each, which means she would pay for 5 sodas and get one free. So the total cost would be:

5 x $0.89 = $4.45

At the local fast food restaurant, the cost of each soda is $0.79, so for 6 sodas, the cost would be:

6 x $0.79 = $4.74.

Therefore, using the loyalty card at the local store is the better deal as Ella would save $0.29 compared to buying the sodas at the local fast food restaurant.

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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