How do I find the first term of geometric progression when the ration is 2 and the sum of the first 6 terms is 7?​

Yes. 64 is a real number. Real numbers can be expressed as infinite decimal expansion.

Real numbers includes integers, natural numbers. Real numbers can be of positive and can be of negative numbers. Real numbers can be both a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers are written as the ratio of two integers. Irrational numbers are not written as the ratio of two integers. Irrational numbers are the type of real numbers. 64 is a real number as well as a perfect square of a number. It is a perfect square of the 8. This explains the properties of Real numbers.

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Answer:

9

Step-by-step explanation:

[tex] | \sqrt{130 \: } | { \: }^{2} \: = |7| {}^{2} + |x| { \\ }^{2} \\ [/tex]

= 130=49+x²

=130-49=x²

=81=x²

[tex] \sqrt{81 \: } = x \\ x = 9[/tex]

Therefore the third side is 9

The track rises 31.88 feet over a horizontal distance.

One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.

Given:

A train track slopes upward at an angle of 12°.

The track rise over a horizontal distance of 150 feet.

From the attached image:

tan(12)° = AB/OA

AB = 150 x tan12°

AB = 31.88 feet.

Therefore, the required distance is 31.88 feet.

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Yes, 7×5×3×2 + 3 is a composite number.

A composite number is a positive integer that has at least one positive divisor other than 1 and itself. In other words, a composite number is a positive integer that can be written as a product of at least two positive integers.

In the number expressed by 7×5×3×2 + 3, we can take 3 as a common factor

7×5×3×2 + 3 = 3(7×5×2 + 1)

So the number has 3 as a factor other than 1 and itself, so it is a composite number.

Also 7×5×3×2 + 3 = 213 = 3×71. So it is not a prime number.

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The subtraction equation the inequality solve is

-9 + -4 = -13

A number line is a horizontal line with uniformly spaced numerical increments.

The number on the line can are represented depending on the numbers that are provided. A number is used to plot a point depending on the question that goes with it and the number type.

For the problem one unit represent a digit number with intervals of 1.

The shorter line is as -4 and the longer is at +9

adding bot together will be

= -9 + -4

= -9 - 4

= -13

hence the subtraction equation is -9 - 4 = -13

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The function f(x) is [tex]-32(x - 2)(x + 2)^2.[/tex].

A linear function has the equation f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, g(x) is a linear function with an x-intercept of 2 (meaning it passes through the point (2,0)) and a slope of 4. So the equation for g(x) would be:

g(x) = 4(x - 2)

A quadratic function has the equation f(x) = [tex]a(x - h)^2[/tex] + k, where (h, k) is the vertex of the parabola. In this case, h(x) is a quadratic function with vertex (-2, -8) and passing through the origin (0, 0) so the equation for h(x) would be:

h(x) = [tex]-8(x + 2)^2[/tex]

Now since f(x) = g(x) ⋅ h(x), we can substitute the equation of g(x) and h(x) in the equation of f(x) to get the equation for f(x) :

f(x) = [tex]g(x) *h(x) = (4(x - 2)) * (-8(x + 2)^2)[/tex]

f(x) =[tex]-32(x - 2)(x + 2)^2[/tex]

So the function f(x) is [tex]-32(x - 2)(x + 2)^2[/tex].

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The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The coordinates of the ordered pair (s) that satisfy all of the system's equations make up the solution set to an equational system. This means that the equations will be true for those x and y values. The intersection of all of the graphs, when a system of equations is graphed, is the solution.

These are the equations:

y = 1.5x - 4

y = -x

Put y = -x in place of y in the first equation.

-x = 1.5x - 4

Assemble similar terms

-1.5x - x = -4

This results

-2.5x = -4

Add -2.5 to both sides.

x = 1.6

Change y = -x to x = 1.6.

y = -1.6

As a result, the system of equations solution is (1.6,-1.6).

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The nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0 is complex number.

The nature of roots of a quadratic equation is determined by the discriminant, which is the value of b² - 4ac. In this case, the quadratic equation is 5x^2 - 2x + 3 = 0.

To find the discriminant, we can use the formula: b² - 4ac. In this case, a = 5, b = -2 and c = 3, so the discriminant is:

Discriminant = (-2)² - 4*5*3 = 4 - 60 = -56

The discriminant can be used to determine the nature of the roots:

If the discriminant is greater than 0, the roots are real and distinct.

If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).

If the discriminant is less than 0, the roots are complex and not real numbers.

In this case, the discriminant is negative, so the roots of the equation 5x^2 - 2x + 3 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).

--The question is incomplete, answering to the question below--

"What is the nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0?"

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To evaluate 1/2yz when y = 3/5 and z = -17/8, we first substitute the given values for y and z into the expression:

1/2(3/5)(-17/8)

Next, we can simplify this by multiplying the fractions:

1/2 * 3/5 * -17/8 = (-3/10) * (-17/8)

To multiply the fractions we multiply the numerators and denominators separately:

(-3/10) * (-17/8) = (-3 * -17)/(10 * 8)

Then we can simplify the numerator by combining like terms:

(-3 * -17)/(10 * 8) = 51/40

So the final result of the expression is 51/40.

Answer:

_51/80

Step-by-step explanation:

1/2*3/5*_17/8

1/2×3/5×(_17/8)

3/10×(_17/8)

_51/80

The y-intercept is 1 at the position (0,1) when x is 0 and y is 1.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

B stands in for the y value of the y-intercept point in the formula.

The y-intercept of a graph is the place where it crosses (or contacts) the y-axis, according to the definition of y-intercept.

The x-coordinate is known to be zero on the y-axis.

Therefore, the equation for determining the y-intercept of a function y = f(x) just requires the substitution of x = 0 and y-solving.

The slope is the ratio of Y change to x change:

Slope = (0-1) / 4-0) = -1/4

Slope = -1/4

When x equals 0, the Y value is known as the Y intercept.

The y-intercept is 1 at the position (0,1) when x is 0 and y is 1.

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The fraction of the watermelons that is ripe is 2 / 5.

The percentage of the watermelons that is ripe is 40%.

The water melons that is not rip is more likely to be picked at random because it is more in number

12 of the 30 watermelons were ripe. The fractions of the watermelon that are ripe can be calculated as follows:

fraction of watermelon that are ripe = 12 / 30

fraction of watermelon that are ripe = 6 / 15

fraction of watermelon that are ripe = 2 / 5

Hence, the percentage of the water melon that are ripe can be calculated as follows:

percentage of water melon that is ripe = 2 / 5 × 100

percentage of water melon that is ripe = 200 / 5

percentage of water melon that is ripe = 40%

If one of the watermelons is picked at random. It is more likely the watermelon that is not ripe  is picked. This is because the unripe watermelon has a higher probability of been picked because it is high in number.

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In the given figure the Δ LHK is similar to ΔL'H'K' and also ΔL'H'K'  is the dilation of  Δ LHK centered at the origin with a scale factor of 3/2.

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Here,
As shown in the figure,
Two triangles are given,
Δ LHK and ΔL'H'K'
Scale factor,
L'H'/LH = L'K'/LK = H'K'/HK = 3/2 [from the figure]

Thus, In the given figure the Δ LHK is similar to ΔL'H'K', and also ΔL'H'K'  is the dilation of  Δ LHK centered at the origin with a scale factor of 3/2.

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Answer: a)False

              b)False

              c)True

              d)True

Step-by-step explanation:

a) the are more crosses marked in the less than  1 mile side (false)

b) the most common one in this is 1/2 mile (false)

c) 5/8 mile is actually empty so it is (true)

d)  this is (true) as the shortest one is 1 therefore 1 x 5 is 5 so it is true

Answer:[tex]\frac{8!}{2!*2!*2!}[/tex] = 5040.

Step-by-step explanation:

Since CALCULUS has 8 letters with 2 indistinguishable C's,

2 indisnguishable L's and 2 indistinguishable U's, the answer is

[tex]\frac{8!}{2!*2!*2!}[/tex] = 5040.

Alex needs to buy x / 3 pots to put 3 flowers in each pot.

What is variable ?

A variable is a value or a quantity that can change or take on different values in a mathematical expression or a scientific experiment. In mathematics and computer science, variables are often represented by letters or symbols, such as x, y, z, etc. These letters or symbols are used to represent an unknown value.

The expression to find the number of pots Alex needs to buy to put 3 flowers in each pot is ,

x = 3 flowers per pot

Number of pots = Total number of flowers / Flowers per pot

Number of pots = x / 3

So, Alex needs to buy x / 3 pots to put 3 flowers in each pot.

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x = 3 flowers per pot

Number of pots = Total number of flowers / Flowers per pot

Number of pots = x / 3

So, Alex needs to buy x / 3 pots to put 3 flowers in each pot.

When a number is multiplied by itself, the result is the perfect square. The same two binomials are multiplied to produce the perfect square trinomial, which is an algebraic expression. This is the first condition to know that a given trinomial is a perfect trinomial.

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Answer: 11

Step-by-step explanation:

Answer:

uh. 11

Explanation:

7 + 4 = 11

The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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The value of the function f ( g ( 6 ) ) = -6

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Let the second function be represented as g ( x )

Now , the value of f ( x ) = 6 - x

The value of g ( x ) = x + 6

To calculate the value of f ( g ( 6 ) )

Substitute the value of x = 6 in the equation , we get

g ( 6 ) = 6 + 6 = 12

Substitute the value of x = 12 in f ( x ) , we get

f ( g ( 6 ) ) = f ( 12 )

The value of the composition function , we get

f ( 12 ) = 6 - 12

f ( 12 ) = -6

Hence , the value of the composition function f ( g ( 6 ) ) is -6

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According to the given quadratic equation  the sum of their pieces:

A. = 8x² + 2x + 10

B. 7x²- 7x -17

C.  incomplete information.

A quadratic equation is a third polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

In mathematics, the quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring." This terminology comes from the fact that a square's area is equal to its side length divided by itself. The Latin term quadrature, which means square, is where the word "quadratic" derives.

A. Lisha

= 3x² + 2x + 8

Makulata = 5x² + 2

Sum of the given equation:

=  (3x² + 2x + 8) + ( 5x² + 2)

=(3x² + 5x² +2x + 10)

= 8x² + 2x + 10

B.

= 4x + 6x² - 11x + 2 + x² - 19

= (6x² + x²) + (4x - 11x) + 2 -19

= 7x²- 7x -17

C. incomplete information.

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The inequality expression and solution to a system of inequalities graphically is xx + yy <= 18

We can represent the system of inequalities as follows:

xx + yy <= 18 (representing the maximum number of pieces of furniture that can be shipped)

A possible solution could be:

xx = 8 (number of tables sold)

yy = 10 (number of chairs sold)

100yy + 450xx >= 3200 (representing the minimum amount of money that must be made from the sale of chairs and tables)

xx >= 8 (representing the minimum number of tables that must be sold)

To graphically represent this system of inequalities, we can begin by graphing the first inequality in a coordinate plane. The inequality xx + yy <= 18 can be represented by a line with the equation y = -x + 18.

Next, we can graph the second inequality. The inequality 100yy + 450xx >= 3200 can be represented by a line with the equation y = -(4.5/5)x + 80.

Finally, we can graph the third inequality, which is a horizontal line at y = 8.

Now we can graph these three inequalities, one line for each inequality, and see where they intersect. The point where all three lines intersect is one possible solution for the system of inequalities.

A possible solution could be:

xx = 8 (number of tables sold)

yy = 10 (number of chairs sold)

However, this solution is within the constraints of the problem and satisfies all three inequalities.

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The vertex, Minima or maxima, Domain and range of the all given graphs are obtained.

For the given question-

Part a:

Vertex : (-1, -4)

Minima or maxima: minima at x = -1

Domain: All real number.

Range: [-4, ∞)

Part b:

Vertex : (3, 4)

Minima or maxima: Maxima at x = 3

Domain: All real number

Range: [4, -∞)

Part c:

Vertex : (4, -4)

Minima or maxima: minima at x =4

Domain: All real number

Range: [-4, ∞)

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The sum of all Payments made during the billing cycle is $975.00

What is the subtractions?

A subtraction is a mathematical operation that is used to find the difference between two numbers. It is represented by the symbol "-" or the word "minus". Subtraction is the inverse operation of addition, meaning that if you add two numbers and then subtract one of those numbers, you should end up with the original value of the other number.

In the FlashCard statement provided, the "DEBITS/CREDITS" section lists all the transactions made during the billing cycle, including payments, purchases, and credits. The payments are listed as negative numbers, indicating that they are subtractions from the balance. The sum of all the payments is calculated by adding up all the negative numbers listed in this section. In this case, it is $975.00.

It's also important to note that this section of the statement lists the transaction made on different days, in the case provided from 4 May to 21 May.

In summary, the sum of all Payments made during the billing cycle is $975.00 which is the total of payments made during that period.

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The lateral surface area of the prism is 81m².

All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.

The total area of all of its faces is reduced to the lateral area. It can also be explained by multiplying the prism's height by the base's circumference.

The base's sides are each 7 meters long, which is a given.

Phase 7+7+7 = 21 meters is the perimeter.

We also know that the prism is 4 meters tall.

The lateral area is therefore

L = P base × h

L = 21m x4m

L = 81m²

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The Law of Cosines states that for a triangle with sides a, b, and c and with angle C opposite side c, the relationship between the sides and the cosine of the angle is:

c^2 = a^2 + b^2 - 2ab * cos(C)

Since the triangle is a right triangle, we can use the Pythagorean theorem to find the value of the angle.

For ∠A:

c^2 = a^2 + b^2 - 2ab * cos(A)

9^2 = 5^2 + 7^2 - 257 * cos(A)

81 = 25 + 49 - 70 * cos(A)

81 = 74 - 70 * cos(A)

81 - 74 = -70 * cos(A)

7 = -70 * cos(A)

cos(A) = -7/70

A = arccos(-7/70)

For ∠B:

a^2 = b^2 + c^2 - 2bc * cos(B)

5^2 = 7^2 + 9^2 - 279 * cos(B)

25 = 49 + 81 - 98 * cos(B)

25 = 130 - 98 * cos(B)

130 - 25 = 98 * cos(B)

105 = 98 * cos(B)

cos(B) = 105/98

B = arccos(105/98)

For ∠C:

b^2 = a^2 + c^2 - 2ac * cos(C)

7^2 = 5^2 + 9^2 - 259 * cos(C)

49 = 25 + 81 - 90 * cos(C)

49 = 106 - 90 * cos(C)

106 - 49 = 90 * cos(C)

57 = 90 * cos(C)

cos(C) = 57/90

C = arccos(57/90)

Keep in mind that the values of the angle are in radians.

Please note that the triangle does not have to be a right triangle, the Law of Cosines works for any triangle.

Answer:

∠ J = 32°

Step-by-step explanation:

the secant- secant angle J is half the difference of the measure of the intercepted arcs, that is

∠ J = [tex]\frac{1}{2}[/tex] (EF - GH) = [tex]\frac{1}{2}[/tex] (123 - 59)° = [tex]\frac{1}{2}[/tex] × 64° = 32°

y=x-1 is the equation of the line in slope intercept form.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The two points from the graph are (1, 0) and (0, -1).

Slope= -1/-1

=1

Now let us find the y intercept.

0=1(1)+b

b=-1

The slope intercept form is y=x-1.

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The range in statistics for a given data set is the difference between the highest and lowest values.

As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.

To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.

For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, The range in statistics for a given data set is the difference between the highest and lowest values.

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Answer:

C. y=x-6

Step-by-step explanation:

x is input

y is output

difference is subtraction

Answer:

C.y=x-6

Step-by-step explanation:

x is input

y is output

output = input - 6

y = x - 6