How do you find the roots of a quadratic equation in factored form?.

The balance at the end of five years is $552.04.

The equation that that represents the balance in the account is $500 x (1.02)^5

The amount of money in the bank account would grow at an exponential rate.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

$500 x (1 + 2/100)^5

$500 x (1.02)^5 = $552.04

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Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.

Follow along with example 343 × 32:

Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.

 3 4 3

 ×3 2

_______

Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.

3 4 3

×3 2

________

6 8 6

Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.

3 4 3

×3 2

__________

  6 8 6

10 2 9×

__________

10 976

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Answer: 1/6

Step-by-step explanation: 2/3 = 4/6

1/2 = 3/6

4/6 - 3/6  = 1/6

The focus of 76-inch diameter and the 42-inch deep reflecting telescope is located approximately 87.92 inches or 7.32 feet from the center of the mirror, at the prime focus.

The focus of a reflecting telescope's mirror is the point where incoming light rays converge after being reflected by the mirror. The location of the focus depends on the size and curvature of the mirror. In this case, the mirror has a diameter of 76 inches and a depth of 42 inches.

This information can be used to calculate the location of the focus, which is approximately 87.92 inches or 7.32 feet from the center of the mirror. This distance is also known as the prime focus and is the point where the image is formed. The eyepiece of the telescope, which magnifies the image formed at the prime focus, is typically located a short distance away from the prime focus, often around 0.90 inches.

The secondary mirror is positioned to reflect light from the prime focus to the eyepiece.

Complete question:

A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.

Primary Mirror

Lighting

Prime Focus

Secondary Mirror

Eyepiece

O1.68 inches

O 87.92 inches

O 512.00 inches

O 8.60 inches

O 0.90 inches

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The product of equation (4y-3)(2y²+3y-5) is 8y³+6y²-29y+15.

According to the question,

The equation is  = (4y-3)(2y²+3y-5)

First, let us start with "4y"

4y×2y² = 8y³

4y×3y =  12y²

4y×(-5 )= -20y

Next, let us multiply by "-3"

(-3)×(2y²) = -6y²

(-3)×3y = -9y

(-3)×(-5) = 15

Now, let us combine all of our values.

The product is = 8y³+12y²-6y²-20y-9y+15

                        = 8y³+6y²-29y+15 (apply BODMAS rule)

So, the product is 8y³+6y²-29y+15.

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The slope of the line 5y = -3x + 10 is -3/5.

To find the slope of the line represented by the equation 5y = -3x + 10, we can first put the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

In this case, we can start by dividing both sides of the equation by 5:

y = (-3/5)x + 2

where (-3/5) is the slope of the line, and 2 is the y-intercept. Therefore, the slope of the line 5y = -3x + 10 is -3/5.

Alternatively, you could have directly found the slope by looking at the x and y coefficients, in this case the slope is -3/5

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The main difference between a mixture and a compound is that a mixture is a physical combination of substances while a compound is a chemical combination of elements.

In chemistry, a mixture is a combination of two or more substances that are not chemically combined and can be easily separated by physical means. The properties of a mixture depend on the properties of the individual substances that make it up, and the substances retain their original properties. Examples of mixtures include air, salt water, and a bowl of fruit.

A compound, on the other hand, is a substance that is made up of two or more elements chemically combined in a fixed ratio. The properties of a compound are different from those of the individual elements that make it up. The atoms in a compound are chemically bonded together and cannot be easily separated by physical means. Examples of compounds include water (H₂O), table salt (NaCl) and sugar (C₁₁H₂₂O₁₁).

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The gradient of the line is 0.

A line's slope is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by the symbols y and x, respectively. where "m" represents the slope of a line. So, tan is the slope of a line.

According to the question

Given the equation of a line is y = -10.

The general equation of the line is y = mx + c

This is a horizontal line because, regardless of the value of x, the value of y is always less than 10. A horizontal line by definition has a slope of:

m = 0

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Answer:

The average marks = 31

Step-by-step explanation:

We know that the average can be measured using mean

Mean = Sum of observations /  no of observations

In the given data no of observations = sum of frequencies

                                                                 = 3+6+10+7+4

                                                                  =30

Sum of observations = No of marks * frequency 1 + No of marks * frequency 2+...

             =  10*3 +20*6+30*10+40*7+50*4

              = 930

Mean = 930/30

          = 31

Answer:

I = 17deg, II = 73deg

Step-by-step explanation:

Let's say first angle is x, and then respectively, the second angle is 4*x + 5.

Their sum is 90 degrees, so:

x + (4*x+5) = 90

5x + 5 = 90

5x = 85 | :5

x = 17 degrees ==> first angle

4*x+5 = 73 degrees ==> second angle

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

In arithmetic, the trigonometric functions (also known as circular features, perspective features, or goniometric functions) are actual features that relate an angle of a proper-angled triangle to ratios of side lengths. they may be extensively utilized in all sciences which might be associated with geometry, such as navigation, strong mechanics, celestial mechanics, geodesy, and lots of others. they are a few of the handiest periodic features, and as such are also extensively used for analyzing periodic phenomena through Fourier analysis.

The trigonometric functions most extensively used in cutting-edge mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. each of these six trigonometric capabilities has a corresponding inverse function and an analog most of the hyperbolic features.

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The correct option is D. Use the distributive property on each side of the equation.

In step with this belongings, multiplying the sum of two or more addends by means of a number will deliver the identical result as multiplying each addend in my view by the quantity after which including the products together. The distributive belongings tell us how to remedy expressions in the form of a(b + c). The distributive belongings are every so often known as the distributive law of multiplication and division.

The Distributive asset is an algebraic asset that states that when an element is improved by means of the sum or difference of terms, it's far essential to multiply every one of the two numbers by means of the element, and subsequently perform the addition or subtraction operation.

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Complete Question:

What is the first step in solving this equation? 3(2x + 6) – 4x = 2(5x – 2) + 6.

A). Use the subtraction property of equality to subtract 6 from both sides. B). Use the addition property of equality to add 4x to both sides.

C). Combine the like terms on each side of the equation.

D). Use the distributive property on each side of the equation.

Samantha is willing to pay up to $72,000 for the 1963 Chevrolet Corvette, which is $17,000 more than Ivan's asking price of $55,000.

It means to receive something from a parent or ancestor through genetic transmission. It also means to receive something as a devise or legacy from an ancestor. inherit an enzyme that is flawed.

Ivan inherited the car and valued it at $45,000, therefore he would make a profit of $17,000 if he sells the car to Samantha.

It's important to note that the final price will depend on the negotiation and agreement between Ivan and Samantha.

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Answer :

HU length = 24

If UVW is Isosceles triangle then UGH is Isosceles

UV=UW = 132

Then,

HU = UG = 24

Answer:

Answers in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note that to ensure the inequality sign are always constant throughout the entire working, otherwise one wrong line will result incorrect answers below it.

The equation which is the best model for a line of best fit for the data is y = ½ x – 1. (Option B)

A line of best fit refers to a straight line which minimizes the distance between it and some data. It expresses a relationship in a scatter plot of different data points. It is an educated guess about where a linear equation which may fall in a set of data plotted on a scatter plot. It is an output of regression analysis and is used as a prediction tool.

The equation of the line can be determined using slope intercept form of the line which is y = mx + b where m is the slope and b is the y intercept. From the given graph, two points which lie on the line of best fit can be used to determine the slope. Let consider two points (2, 0) and (0, -1). Hence

m = (-1 – 0)/(0 – 2) = -1/-2 = ½

The value of y intercept is -1 (when x = 0)

Hence, the equation is:

y = ½ x - 1

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Plot the lines and shade in the regions on the same x-y plane to find the solution to the system of inequalities 4x+6y ≤ 24 and x + 5y ≤ 10 fall under the mixed shaded region in the graph.

What is the linear inequalities?

Linear inequalities are mathematical expressions that describe a relationship between two variables that is linear in nature. The most common form of a linear inequality is of the form ax + by < c, where a, b, and c are constants and x and y are variables.

Yes, this system of two linear inequalities can be represented graphically on the x-y plane by plotting the solutions to each inequality. The steps are as follows:

        4x + 6y <= 24

        => -6y <= -4x + 24

        => y >= (4/6)x + 4

        => y = (4/6)x + 4

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The recursive formula represents the total amount of money in Victoria’s account at the end of the nth year

Generally, The recursive formula representing the total amount of money in Victoria's account at the end of the nth year is:

A(n) = A(n-1) + 15 + 0.02 * A(n-1)

where

To get the first value of A(n) we can use the initial condition

A(1) = 200 + 15 + 0.02 * 200

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A) The time in minutes that it would reach 40% charge is; 48 minutes

B) The percent at 1 hr 48 minutes is; 90%

The general form of the equation of a line in  slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given parameters, we can find the slope from the formula;

m = (y2 - y1)/(x2 - x1)

m = (30 - 10)/(36 - 12)

m = 20/24

m = 5/6

Thus, for a 40% charge, we have;

5/6 = (40 - 30)/(t - 36)

Cross multiply to get;

5(t - 36) = 60

t - 36 = 12

t = 48 minutes

B) After 1 hr 48 minutes or 108 minutes, it means that;

Percentage = 5/6 * 108

= 90%

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The y-intercept for the graph of this line 3x-5y=6 is -6/5.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

To determine the intercept of the equation, it would be helpful to write it in its slope-intercept form which is expressed as:

y = mx + b

where m is the slope and b is the y-intercept. Therefore, the value of b would be the correct answer here.

3x-5y=6

5y=3x - 6

y = 3x/5 - 6/5

Thus, the y-intercept is -6/5.

Thus, the y-intercept for the graph of this line 3x-5y=6 is -6/5.

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the mid point of the side AB is (0,-1).

What is triangle?

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. A triangle's area is the region that each of its sides touches. A triangle's area varies from one triangle to another depending on the size of its sides and internal angles. Triangle area is measured in square units like m2, cm2, and in2.

A = (2,-3)

B = (-2,1)

Mid point will be 1+3/2, -2-2/2

Mid point is (0,-1)

Hence the midpoint of the side AB is (0,-10).

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Answer: The domain of g(x) = √(x - 3) is (3, ∞) because the square root function is defined for non-negative numbers, x - 3 must be greater than or equal to 0, which means x must be greater than 3.

The range of g(x) = √(x - 3) is (0, ∞) because the square root function can only output non-negative numbers, and as x increases, the value of √(x - 3) will also increase.

So the correct answer is: D: (3, ∞) and R: (0, ∞)

Step-by-step explanation:

The domain of the given function is Domain: [3,∞),{x|x≥3} and the range is Range: [0,∞),{y|y≥0}. Therefore, the option A is the correct answer.

The given function is g(x)=√(x-3).

We know that, the domain is set of all x-values and the range is set of all y-values.

Substitute x=1, 2, 3, 4,.....in the given function, we get

g(1)=√(1-3) = i√2

g(7)=√(7-3) = 2

g(19)=√(19-3) = 4

So,

Domain: [3,∞),{x|x≥3}

Range: [0,∞),{y|y≥0}

Therefore, the option A is the correct answer.

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Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

What is yard ?

A yard is a unit of length measurement in the U.S. customary system and the imperial system. It is equal to 3 feet or 36 inches. The symbol for yard is "yd". It is mostly used in the United States and the United Kingdom for measuring small lengths, such as in construction, textiles, and landscaping.

Carl has three lengths of cable, 5/6 yard long, 1/4 yard long and 2/3 yard long. The total length of the cable that Carl has is:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

To check whether he has at least one yard of cable or not, we need to compare the total length of the cable he has (2 5/36 yard) with 1 yard. Since 2 5/36 is greater than 1, it means he has more than 1 yard of cable. So, he will have at least 1 yard of cable left after using some of it.

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

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Carl has three lengths of wire, each measuring 5/6 yards, 1/4 yards, and 2/3 yards. The wire that Carl has measures a total of:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

We need to compare the entire length of the cable he has (2 5/36 yard) with 1 yard to see if he has at least one yard of cable or not. He has more than one yard of cable since 2 5/36 is larger than 1, which is greater than 1. After using some of the wire, he will still have at least 1 yard of it.

Answer:

Mini golf costs: $10.00 per round.

Batting cages cost: $2.50 each turn.

Step-by-step explanation:

Let g= rounds of golf

Let b = batting cage

Sylvester

5g+4b = 60

Lin

3g +6b = 45

We have two equations and two unknowns

5g+4b = 60

3g +6b = 45

Divide the second equation by 3

3/3g +6/3b = 45/3

q+2b = 15

Multiply this equation by -2

-2q -4b= -30

Add this to the first equation

5g+4b = 60

-2q -4b = -30

3q = 30

Divide by 3

3g/3 = 30/3

g = 10

A game of mingolf is 10 dollars

Now we need to find b

q+2b = 15

10 +26 =15

Subtract 10

10-10+2b =15-10

26=5

Divide by 2

2b/2 =5/2

b=25

A turn in the batting cage is 2.50

There are 21 states landlocked and 27 states do not border an ocean.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since there are 48 states in the continental United States, some of which are on the border of an ocean and some of which are not.

According to the question,

The ratio of the states having the border to the ocean and not having the border to the ocean = 7 : 9

Let the states having the border to the ocean = 7x

The states do not have a border to the ocean = 9x

Thus, 7x + 9x = 48

⇒ 16x = 48

⇒ x = 3

So, the states do not have a border to the ocean = 7 × 3 = 21

And, the states do not have a border to the ocean = 9 × 3 = 27

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The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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Answer:

3.2

Step-by-step explanation:

......................

The probability that a student picked from this group at random is using a pen or pencil is 19/21

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, in a group of 42 students, 17 use pens for writing and 21 use pencils for writing.

P(A or B) = P(A) + P(B)

P(A) = 17 / 42

P(B) = 21 / 42

P(A or B) = 17 / 42 + 21 / 42

P(A or B) = 38 / 42

P(A or B) = 19/21

Hence, the probability that a student picked from this group at random is using a pen or pencil is 19/21

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