Use the series formula to find the sum of the geometric sequence -5,15,45,135 Use the series formula to find the sum of the geometric sequence. Find the sum of the first 10 terms.

The date which is 100 days ago from 12 February 2023  is equal to

November 04, 2022 .

Present date is equal to 12 February 2023.

Date which is 100 days is written as :

January month has 31 days.

December month has 31 days.

November month has 26 days.

Total days equal to :

( 31 + 31 + 26 + 12 ) days = 100 days

100 days ago from 12 February 2023 is equal to :

12 February 2023  minus 100 days is 04 days 2022.

Therefore, the day which is 100 days ago from 12 February 2023 is given by   November 04, 2022 .

The above question is incomplete , the complete question :

What is 100 days ago from 12 February 2023 ?

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Answer:

  C.  4x²√(3x)

Step-by-step explanation:

You want to simplify √(48x⁵).

Square root expressions can be simplified by removing perfect squares from under the radical:

  [tex]\sqrt{48x^5}=\sqrt{16x^4\cdot3x}=\sqrt{(4x^2)^2}\cdot\sqrt{3x}=\boxed{4x^2\sqrt{3x}}[/tex]

Answer:

-49,152

Step-by-step explanation:

if you multiply -0.75, times 4 it equals -3 so do that until you get the ninth term. (Multiply each term by 4).

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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The name of the equation for the regression line is the Regression Equation.

Regression Line:

Regression is a statistical technique used in finance, investing, and other fields that attempts to determine the strength and nature of the relationship between one dependent variable (usually denoted Y) and several other variables (called independent variables).

Simple linear regression:

Y = a + bX+ u

​Multiple linear regression:

Y = a + b₁ X₁ + b₂ X₂ + b₃ X₃ +..... + bₙ Xₙ +u

where:

Y = The dependent variable that can be predicted.

X =The independent variables that are used to predict

a = The y-intercept

b (beta coefficient) = is the slope of the independent variable(s)

u = The error term

​Regression equation:

Regression equations are used in statistics to determine if there is any relationship between data sets. For example, if you measure a child's height every year, you'll find that they grow about 3 inches each year. This trend (growth of 3 inches per year) can be modeled using a regression equation. In fact, most things in the real world (from oil prices to hurricanes) can be modeled with a few equations. You can predict future events.

There are several types of regression equations. Some of the more common ones include exponential and simple linear regression (to fit data to an exponential or linear equation). The regression equation most likely to be encountered in elementary statistics takes the form of a linear one.

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a). The expression which correctly represents the length of the rectangular area is; 4x - 5.

b). The product of the length and width of the rectangle is; (4x - 5) 3x = 12x² - 15x.

Recall; for rectangles;

Area = length × width

Therefore, Length= Area / Width

Length = 12x² - 15x / 3x

Length = 4x - 5

Therefore, the expression which represents the length is; 4x - 5.

b) By multiplying the length and width of the rectangular area; we have;

Area = (4x - 5) 3x

= 12x² - 15x

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Answer: CDE can describe a minor arc, a major arc, a semicircle, or a chord, depending on the context in which it is used. Here are the definitions of each of these terms:

A minor arc is an arc of a circle that is smaller than a semicircle. It is named after the two endpoints of the arc. So, CDE would be a minor arc if it is a part of a circle.

A major arc is an arc of a circle that is larger than a semicircle. It is also named after the two endpoints of the arc. So, CDE would be a major arc if it is a part of a circle and spans more than 180 degrees.

A semicircle is an arc of a circle that is exactly half of the circle. It is named after the two endpoints of the diameter that it cuts. So, CDE would be a semicircle if it is a part of a circle and spans exactly 180 degrees.

A chord is a line segment that connects two points on the circle. It is named after the two endpoints of the segment. So, if CDE is a line segment that connects two points on a circle, then it would be a chord.

Step-by-step explanation:

Answer:

200 km

Step-by-step explanation:

Let's use the formula:

distance = rate × time

Let the original average speed of the car be r km/h, and let the distance between the two cities be d km.

According to the problem, the car takes 2 hours to cover the distance, so we have:

d = r × 2

If the car's average speed decreased by 20 km/h, its new average speed would be (r - 20) km/h. If it took 30 minutes (0.5 hours) longer to cover the same distance at the slower speed, we have:

d = (r - 20) × 2.5

Now we have two equations for d:

d = r × 2

d = (r - 20) × 2.5

We can solve for r in the first equation:

r = d / 2

Substituting into the second equation:

d = (d/2 - 20) × 2.5

Simplifying:

d = 1.25d - 50

0.25d = 50

d = 200

Therefore, the distance between the two cities is 200 km.

꧁༒αηѕωєяє∂ ву gσ∂кєу༒꧂

Answer:

Variable p represents "the puppy is tired", and variable q represents "the puppy will sleep".

The statement in symbolic form is: p → q, where the symbol → means "implies" or "if...then".

Note that the complete proof that ∠A ≅ ∠D is given as follows:

Note that the Alternate Interior Angles Theorem states that when two parallel lines are crossed by a transversal, the alternate interior angles are congruent.

The Basic Proportionality Theorem states that in a triangle, a line parallel to one side divides the other sides proportionally.

The Vertical Angles Theorem states that vertical angles are congruent.

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The probability of rolling a 7 with a pair of dice is 1/6. This is because there are six possible combinations that add up to 7.

Each of these combinations has an equal probability of occurring, so the probability of rolling a 7 is 1/6. (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

To explain further, when two dice are rolled, there are 36 possible outcomes, each with an equal probability of occurring. Of the 36 outcomes, 6 of them will result in the total number of dots appearing on top being 7. Since 6 out of 36 outcomes result in a 7, the probability of rolling a 7 is 6/36 or 1/6. This means that if two dice are rolled 36 times, there is a 1 in 6 chance that the total number of dots appearing on top will be 7 at least once.

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The 1 meter is 3.28084 feet.

Since 1983, the meter has been internationally defined as the length of the path traveled by light in a vacuum in 1/299,792,

58 seconds. This definition can be applied easily and precisely with modern techniques, and the speed of light is considered a universal constant, making it an ideal  basis for a standard of length.

foot, plural of feet, measured by a number of  ancient, medieval and modern linear measurements (usually 25–3

cm) based on the length of a human foot, used exclusively in English-speaking countries, where it usually consists of 12 inches. , or a third of a yard.

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Answer:

D

Step-by-step explanation:

draw a right triangle, with the segment being the hypotenuse. Use Pythagorean theorem to calculate.

to use pythagorean Theorem

Step-by-step explanation:

The Pythagorean Theorem is a formula that allows you to calculate the distance between two points in a coordinate plane. It states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of two points on a coordinate grid, the distance between them is the length of the hypotenuse of the right triangle formed by the horizontal and vertical distances between the two points.

The cost will be $504.00 to buy enough carpet for Zach's living room.

To determine the cost of the carpet for Zach's living room, we first need to calculate the area of the room. The area of a rectangle is found by multiplying the length by the width. In this case, the length is 9 yards and the width is 8 yards:

Area = 9 yards × 8 yards = 72 square yards

Now that we know the area of the room, we can calculate the cost of the carpet. The carpet costs $7.00 per square yard, so we multiply the area of the room by the cost per square yard:

Cost = 72 square yards × $7.00 per square yard = $504.00

Therefore, it will cost $504.00 to buy enough carpet for Zach's living room.

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A rectangle of 24 1/2 sqaure feet if the length of the rectangle is 4 3/8 feet, and the width of the rectangle is 4 feet.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

To find the width of the rectangle, we can use the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 24 1/2 square feet and the length is 4 3/8 feet. Substituting these values into the formula, we get:

24 1/2 = 4 3/8 x Width

To solve for the width, we can first convert both mixed numbers to improper fractions:

24 1/2 = 49/2

4 3/8 = 35/8

Substituting these values, we get:

49/2 = 35/8 x Width

To solve for Width, we can cross-multiply:

49/2 * 8/35 = Width

Simplifying, we get:

4 = Width

Therefore, the width of the rectangle is 4 feet.

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15/32 inches is equivalent to 11.90625 mm

Unit conversion is the process of converting a quantity from one unit of measurement to another. The unit conversion method involves multiplying the original quantity by a conversion factor that expresses the relationship between the original unit and the desired unit.

1 inch =  25.4 mm

1 mm = 0.1 cm

We have 15/32 inch

Converting the fraction into decimal part, we obtain 0.46875 inch

Now, 0.46875 inch = 0.46875 * 25.4 mm

                                 = 11.90625 mm

                                 = 11.90625 * 0.1 cm                

                                  = 1.190625 cm

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1.5 liter is 0.396258 gallons.

A gallon is a unit of volume in imperial units and US standard units. Three different versions are currently in use:

imperial gallon (imp gallon), defined as

.5

609 liters, is or was used in Great Britain, Ireland, Canada, Australia, New Zealand and some Caribbean countries;

US gallons (US gallon), defined as 3.785

1178

L,[1] (231 cubic meters), used in the United States and some Latin American and Caribbean countries; and

US dry gallons ("usdrygal"), defined as 1⁄8 US Bushel (exactly

.

0

88377086 L).

There are two pints in a liter and four liters in a gallon. Different sized pints correspond to different sized imperial and US gallons.

The IEEE standard symbol for both US (liquid) and imperial gallons is gal [2], different from gal (symbol: Gal), the CGS unit of acceleration.

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The equation for the height of the trapezoid is 402.8 = (1/2)h(14.6 + 35.4)

The formula for the area of a trapezoid is:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the two bases.

We can use this formula to write an equation to determine the height of the trapezoid

When the known values are substituted, we have

402.8 = (1/2)h(14.6 + 35.4)

Hence, the equation is 402.8 = (1/2)h(14.6 + 35.4)

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The two different ways to find the product of 239×64 are,

(240 - 1)×64 and 239×(60 + 4).

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, A product of 239×64.

The first way is,

239×64.

= (240 - 1)×64.

= 15360 - 64.

= 15296.

Another way to find the product of 239×64 is,

= 239×(60 + 4).

= 14340 + 956.

= 15296.

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please make me brainalist and keep smiling

75% of 500 is determined using bar model as 375.

To use a bar model to find 75% of 500, you can follow these steps:

3 parts x 25% per part = 75%

Finally, to find the value of 75% of 500, you can multiply 500 by 75% in decimal form (0.75):

500 x  0.75 = 375

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Therefore , the solution of the given problem of function comes out to be is that the function approaches negative infinity as x approaches positive or negative infinity.

The mathematics curriculum covers the study of number and their variable as well as our surroundings, architecture, and both actual and hypothetical locations. The link between the amounts of inputs as well as the associated outputs for each is shown graphically by a function. A function is, to put it simply, a group of inputs whose, when combined, result in particular outputs for every input. Each role is assigned a region, locale, or range .

Here,

Given :

f(x) = -x² + 14x³ - 24x⁷ - 10x¹² + 22x⁴ - 18x¹¹ + 4x⁴  +21

To describe the end behavior of the given polynomial function f(x), we only need to consider the term with the highest degree, which is - 10x¹²

Since the degree of the term is even and the coefficient is negative, we know that as x approaches positive or negative infinity, the function will also approach negative infinity.

Therefore, we can say:

As x to -∞, f(x)  to - ∞

As x to +∞, f(x) to-∞

So the end behavior of the function

f(x) = -x² + 14x³ - 24x⁷ - 10x¹² + 22x⁴ - 18x¹¹ + 4x⁴  +21

is that the function approaches negative infinity as x approaches positive or negative infinity.

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Answer:

3528

Step-by-step explanation:

49*72=3528

Answer:

Step-by-step explanation:

49x 72

Answer:

The answer is: K = 14.

The two possible locations of point B on the number line are 0.1 and 1.1.

A number line is a graphic depiction of numbers organized in a straight line in mathematics. Positive numbers appear to the right of zero and negative numbers to the left of zero when it is displayed horizontally. At the line's intersection, the number zero serves as a standard against which other numbers' magnitudes can be measured.

Many forms of numbers, including whole numbers, integers, fractions, decimals, and even irrational numbers, can be represented on a number line. The distance between any two points on the number line, which stands for the difference between any two matching numbers, corresponds to a distinct number.

Number lines are frequently used to graph functions and equations as well as to execute basic arithmetic operations including addition, subtraction, multiplication, and division. They are also helpful for comprehending ideas like magnitude, distance, and absolute value.

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The method to convert milimeter to meters will be through multiplication of [tex] {10}^{-3} [/tex] with the quantity in milimeter.

The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.

Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -

Quantity in meters = quantity in milimeter ×

[tex] {10}^{-3} [/tex], where [tex] {10}^{-3} [/tex] has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.

So, quantity in meter = 10⁹ × [tex] {10}^{-3} [/tex],

Performing multiplication which will be done through subtraction of powers

Quantity in meters = 10⁶ meters

Hence, mm to meters will be multiplication with [tex] {10}^{-3} [/tex].

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Therefore , the solution of the given problem of linear equation comes out to be  129 sodas were sold.

The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's start by defining some variables. Let s be the number of sodas sold and h be the number of hot dogs sold.

We know from the problem that:

s + h = 172 (the total number of sodas and hot dogs sold)

s = 3h (the number of sodas sold is three times the number of hot dogs sold)

We can substitute the second equation into the first equation to eliminate s and get an equation in terms of h:

3h + h = 172

4h = 172

h = 43

So, 43 hot dogs were sold. We can then use the second equation to find the number of sodas sold:

s = 3h = 3(43) = 129

Therefore, 129 sodas were sold.

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Answer:

x = 3 units

Step-by-step explanation:

These two triangles are similar figures, which means the ratio of the lengths of their corresponding sides are equal:

[tex]\frac{Side AB}{Side AC} = \frac{Side DE}{Side CE}[/tex]

= [tex]\frac{24}{2x} = \frac{56}{3x + 5}[/tex]

Cross-multiplication is applied:

= [tex](24)(3x + 5) = (56)(2x)[/tex]

Parenthesis are expanded by using the Distributive Law:

= [tex]72x + 120 = 112x[/tex]

Bring all the like terms together and then isolate x:

= [tex]120 = 112x - 72x[/tex]

= [tex]120 = 40x[/tex]

= x = [tex]\frac{120}{40}[/tex]

∴ x = 3 units