consider the following modification of the initial value problem in example 3.4.2

The equation in slope-intercept form is y = (-2/5)x - 9/2.

Slope-intercept form is an equation of a line that is written in the form of y=mx+b, where m is the slope of the line and b is the y-intercept. The slope-intercept form makes it easy to identify the slope and y-intercept of a line from an equation.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Therefore, for a line with a slope of −2/5 that passes through the point (15, −9/2), we can solve for b using the point-slope formula.
Point-slope formula:  y - y1 = m(x - x1)
Plugging in the given information, we get:
-9/2 - (-9/2) = (-2/5) (15 - 15)
Solving this equation yields b = -9/2.
Therefore, The equation in slope-intercept form is y = (-2/5)x - 9/2.

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Answer:

<a=113, <b=67, <c=126, <d=54

Step-by-step explanation:

<a= 180-67=113 degrees. Why? Angles on a straight line add up to 180

<b=67 degrees Why? Because it is an alternate interior angle with 67degrees and alternate interior angles are equal

<d = 54 degrees Why? Because it is an alternate interior angle with 54 degrees and alternate interior angles are equal

<c=180-54=126 degrees Why? Because it is a co-interior angle with <d which is 54 degrees and co-interior angles add up to 180 degrees

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The compound inequality given is "and" inequality.

Compound inequalities are inequalities which consist of more than two expressions connected with two or more inequality signs.

Compound inequality can be divided into two or more simple inequalities.

"And" inequalities are those compound inequalities where both the inequalities need to be true for the statement to be true.

"Or" inequality needs only any one of them true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 throughout,

5 > x > 2

Here x lies between 2 and 5 where x > 2 and x < 5.

Hence this inequality is "and" inequality.

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The expression that shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down is t = (240 - (v/120) * 240) / (120 - v)

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The relation between time, t, and the speed at which Rashid slows down, v, is given by the formula:

t = (240 - (v/120) * 240) / (120 - v)

t = time

v= speed.

This formula can be derived by using the distance formula (distance = speed x time) and the fact that the distance traveled is constant (240 km).

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The center point formula,  (x h) 2 + (y k) 2 is r, must be converted into standard form in order to get the center and radius. 2 (x-h)2 + (y-k)2 is r2 (x-h)2 + (y-k)2 =is r2).

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The polynomial function in given graph for g(x) is

g(x)= -x^2.

What are polynomial functions?

Polynomial is made up of two words, poly and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms"

Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants. for e.g.

f(x) = 3x^2 - 5.

Types of Polynomial Function:

Constant Polynomial Function -  A constant polynomial function is a function whose value does not change. It remains the same and also it does not include any variables.

Zero Polynomial Function - Polynomial functions with a degree of 0 are known as zero Polynomial functions.

Linear Polynomial Function - Polynomial functions with a degree of 1 are known as Linear Polynomial functions.

Quadratic Polynomial Function - Polynomial functions with a degree of 2 are known as Quadratic Polynomial functions.

Cubic Polynomial Function - Polynomial functions with a degree of 3 are known as Cubic Polynomial functions.

Quartic Polynomial Function - Polynomial functions with a degree of 4 are known as Quartic Polynomial functions.

Now,

In given graph, We fill find g(x) by putting value of x and seeing the corresponding result of y.

As for    x      y is

            1       -1

             2      -4

            3       -9

            -1       -1

            -2      -4

Therefore, from given values we can conclude that polynomial function for g(x)= -x^2.

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The range of possible values of the third side of the triangle is 3 < x < 25. That is, the possible whole number values are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24.

From the given information, we are to determine all possible values for the length x of the third side of the given triangle

From the given information,

One of the sides of the triangle is 11 centimeters in length

and

The length of the other side is 14 centimeters

From one of the properties of a triangle,

The third of a triangle is greater than the positive difference of the other two sides and the third side is lesser than the sum of the other two sides.

if the third side of the triangle is x

Then,

x < 14 + 11

x < 25

and

x > 14 - 11

x > 3

Thus,

x > 3 and x < 25

3 < x and x < 25

3 < x < 25

Thus, the range of possible values is 3 < x < 25.

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The vertex of the function is at (5, 10) .For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

Vertex, domain and range of a function

The vertex of a quadratic or linear function is in the form

y =  a(x – h)^2 + k

where;

(h, k) is the vertex of the function

Given the function expressed as;

f(x) = |x-5| + 10

On comparison, you can see that h = 5 and k =10, hence the vertex of the function is at (5, 10)

For the domain and range

Domain are the dependent variable for which a function exist while the range is the independent variable for which a function exist.

For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

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On solving the provided question, we can say that the - by solving algebraic equation x= 0 and y= 4.

A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Check out algebraic expressions as well. Equations, or the equal sign, simply indicate equality. With mathematics, and algebraic expression is one that is constructed using variables, constant algebraic numbers, and algebraic operations. An algebraic expression is, for instance, 3x2 2xy + c.

y+ (2/3)x = 4

12—3y

3y +6x 12

2x+3y=12

by subtracting2frorn1.

4x=o

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Each member would receive 0.8 pizza.we divided the number of pizzas (400) by the number of members (5) to get 8.

1. Divide the number of pizzas (4) by the number of members (5): 4 ÷ 5 = 0.8

2. Each member would receive 0.8 pizza.

Each member would receive 8 pizza.

1. Multiply the number of pizzas (4) by the number of members (100): 4 x 100 = 400

2. Divide the number of pizzas (400) by the number of members (5): 400 ÷ 5 = 8

3. Each member would receive 8 pizza.

If The Robotic team ordered 4 pizza and only 100 members showed up, each member would receive 8 pizza if the pizzas are shared equally. To calculate this, we first multiplied the number of pizzas (4) by the number of members (100) to get 400. Then, we divided the number of pizzas (400) by the number of members (5) to get 8. Therefore, each member would receive 8 pizza.

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Dilation rules refer to the mathematical rules and formulas used to calculate the image of a point, shape, or figure after it has undergone a dilation transformation.

Here are some of the most common dilation rules:

It's important to note that, the rules mentioned above are general rules of dilation and they might vary depending on the specific dilation transformation.

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The length of each piece of fabric is, 3/4 yards.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are 3 pieces of fabric.

And, The total length of the pieces of fabric is 2 1/4 yards.

Here,  Each piece of fabric is the same length.

Hence, The length of each piece of fabric is,

⇒ 2 1/4 ÷ 3

⇒ 9/4 × 1/3

⇒ 3/4 yards

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The expression which can be rewritten as (x+7)(x - 1) as required in the task content is; Choice C; (x+3)²-16.

It follows from the task content that the expression which can be rewritten as ( x + 7 ) ( x - 1 ) be determined.

By polynomial expansion, the expression (x+7)(x - 1) can be written as;

x² + 7x - x - 7

= x² + 6x - 7.

By observation, it follows that the expression which seems to have a degree of 2 is; (x + 3)² - 16.

On this note, by checking; we have;

x² + 6x + 9 - 16

= x² + 6x - 7

Ultimately, the expression which could be rewritten as (x+7)(x - 1) and is to be identified is; Choice C; (x + 3)² - 16.

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Answer:  2.78 Yards, 8.33 ft,

Step-by-step explanation:

Answer:

100 in. = 100 inches, 8 feet 4 inches, or 2.77777777778 yards.

Step-by-step explanation:

Water fills the cone to a capacity of 75%. 0.75 is the decimal equivalent of 75%.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question-

volume of water  =  (3/4) * (1/3)(a)(h)

volume of water  =  (3/4) * volume of cone

volume of water  =  75% of the volume of cone

75% of the cone's volume is filled with water.

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In general, a larger sample size is more likely to represent the population than a smaller sample size. This is because a larger sample size increases the chances that the sample will be representative of the population.

When the sample size is that larger, there is a lower chance of getting a skewed or biased sample. A larger sample size also tends to have less variability in the sample statistics, making it more likely to provide accurate estimates of population parameters.

However, it is important to note that increasing the sample size does not guarantee that the sample is representative of the population. The sampling method used, and the way the sample is selected, can also have an impact on the representativeness of the sample.

Hence, surveying 100 students is more likely to represent the population than surveying a smaller sample size like 10 students, but it does not guarantee a perfect representation of the population.

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Answer: To find out which loan option will have the least interest, you need to calculate the interest amount for each option. You can do this by using the formula:

Interest = Principal x Interest Rate x Time (in years)

For option A, the interest amount would be:

Interest = $12,000 x 0.05 x (48/12) = $2,400

For option B, the interest amount would be:

Interest = $12,000 x 0.045 x (60/12) = $3,000

For option C, the interest amount would be:

Interest = $12,000 x 0.0375 x (66/12) = $2,970

For option D, the interest amount would be:

Interest = $12,000 x 0.04 x (72/12) = $3,840

As we can see the lowest interest amount is option C which is $2,970. Thus Ciara will pay the least interest if she chooses option C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To write 45.52 as a fraction you have to write 45.52 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

45.52 = 45.52/1 = 455.2/10 = 4552/100

And finally we have:

45.52 as a fraction equals 4552/100

When we decrease the exponent of 10 by 1, the number becomes one-tenth of the previous number.

For the fixed base(10), if the exponent decrease by 1, the number will becomes one-tenth of the previous number.

The Power Rule for Exponents is (a^m)^n = a^m*n. To increase a number with an exponent to a power, we need to multiply the exponent times the power. Negative Exponent Rule is x^-n = 1/x^n. We need to invert the base to change a negative exponent into a positive.

Exponents are used to represent repeated multiplication of a number by itself. For example, 7 * 7 * 7 can be showed as 73. Here, the exponent is 3 that stands for the number of times the number 7 is multiplied. The base here is 7 that is the actual number which is getting multiplied. So, initially exponents or powers shows the number of times a number can be multiplied. If the power is 2, it means the base number is multiplied two times with itself.

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The average rate of change of the given function is 20.

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The average rate of change of a function f(x) over the interval [a,b] is given by the formula:

(f(b) - f(a)) / (b - a)

So, for the function f(x) = x² + 2 as x changes from 5 to 15, we can plug in the values to find the average rate of change:

(f(15) - f(5)) / (15 - 5) = (15² + 2 - 5² - 2) / (15 - 5) = (225 - 25) / 10 = 200 / 10 = 20

So the average rate of change of the function is 20.

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A linear function is one that visualizes a straight line on the coordinate plane.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear. A linear function is, for instance, the progression in the number of ticks of a clock's second hand through time.

Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y.

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According to the Common Segments Theorem, if a segment is merged with two congruent segments, the subsequent segments will also be congruent

a piece removed from a geometric form by one or more points, lines, or planes. Examples include the region of a circle enclosed by its chord and arc, or the portion of a sphere enclosed by two parallel planes. Segment is a service that makes it easier to acquire and use data from users of your digital domains because it is a customer data platform (CDP) (websites, apps, etc). Your first-party customer data may be gathered, transformed, sent, and archived using Segment. between two points on a line or curve; a segment. a segment of a solid figure or plane that is removed by an intersecting line.

given

According to the Common Segments Theorem, if a segment is merged with two congruent segments, the subsequent segments will also be congruent.

The overlapping segments that result are congruent if two collinear segments that are next to a common segment are also congruent. Intermingling Angle Theorem.

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Answer:

y = 43, x = 23

Step-by-step explanation:

[tex]180 - 63 = 3y - 12\\117 = 3y - 12\\129 = 3y\\y = 43[/tex]

Supplementary angles add up to 180 and alternative angles (Z-pattern) are the same

[tex]180 - 63 = 5x + 2\\117 = 5x + 2\\115 = 5x\\x = 23[/tex]

Yes, the given equation y = 10x is a direct variation.

Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity. This means that if one quantity increases then the other quantity will also experience a proportionate increase.

Similarly, if there is a decrease in one quantity then the other quantity also decreases. Direct variation is a linear connection hence, the graph will be a straight line. Further, if the two entities are in a direct variation relationship then one will be a constant multiple of the other.

A direct variation equation has the form

y = kx  

Here, k is the constant of variation

Now, y = 10x is in this form, thus it is a direct variation.

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When the slope is given as 2, the result of the slope intercept form is y = 2x + c where m stands for the slope and c for the y-intercept .

The intersection point is the location on the y-axis where the slope of the line crosses. where the y-axis crosses that point on a line or curve. By using y = mx+c as the equation for the straight line, where m stands for the slope and c for the y-intercept, this is proven. The slope (m) and y-intercept (b) of the line are denoted in the intercept form of the equation. For equations of the intercept form (y=mx+b), the slope and y-intercept, respectively, are m and b. Furthermore, some equations may be rewritten to appear as slope intercepts. For instance, the slope and y-intercept change to 1 and 0 respectively when y=x is represented as y=1x+0.

given

slope ( m ) = 2

= y = 2x + c

When the slope is given as 2, the result of the slope intercept form is y = 2x + c.

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Answer:

See below

Step-by-step explanation:

Since lines n and p intersect, they must have different slopes.  Lets say they have slopes 2 and 4, as an example.  They will intersect.  Lines m and l are perpendicular to n and p, so their slopes will be the negative inverse of 2 and 4.  That gives them slopes of -(1/2) and -(1/4).  These slopes are different, so they will intersect.

The attached graph illustrates this intersection with lines having the above slopes.  Lines m and l intersect at (-1,1) in this example.  Lines m and l also intersect, off the graph at the top left.

The statement '15 more than the sum of 5 and a number' is equivalent to the mathematical expression (5+n)+15.

Therefore the answer is (5+n)+15.

The statement "15 more than the sum of 5 and a number" is asking for an expression that represents the value that is 15 greater than the result of adding 5 and a number together. The mathematical way to express this is:

15 + (5 + n)

Where n is the number that we are adding to 5.

15 is being added to the sum of 5 and n. The parentheses around the 5 and n indicate that those two values are being added together before the 15 is added to them.

In other forms of representation

15+(5-n) or (5+n)+15 or (5-n) +15 or 15+5n does not convey the meaning you want it to convey as these forms does not represent "15 more than the sum of 5 and a number"

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It defines conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

Estimation refers to obtaining a result that is close to the correct or actual result. It involves conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

There are various reasons, the estimate is especially useful when there is not enough information to calculate an exact value. Accountants use estimates when they want to calculate transaction amounts.

To estimate the quotient, we round the dividend to the nearest tens, hundreds, or thousands.

There are two methods for estimating the quotient:

let us consider an example:

for 371 nearest value is 400 because in the tens place it is equal to 400.

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