Solve the following quadratic-like equation.

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0[/tex]

Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.

The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.

If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".

So, the total length of the wire is:

 [tex]5x = 2.5[/tex] meters

To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.

Therefore, the length of the longer part of the wire is:

[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]

Therefore, the measure of the longer part of the wire after cutting is 2 meters.

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The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.

The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.

The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.

The graph represents a function because for every value of time, there is exactly one corresponding value of depth.

The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.

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Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:

4

Step-by-step explanation:

f(-1) = 2

g(2)= 4

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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Problems:

Solve for x: 2x - 5 > 9x + 2

Solve for x: 3x + 2 < 7x - 5

Solve for x: 4x + 3 < 2x - 1

Solve for x: -2x - 4 > -8x + 3

Solve for x: 5x + 1 < 2x + 7

Answers:

x < -0.7

x > 1.75

x < -1

x < 0.875

x < 1.2

Answer:  

Example 1

Solve 3x − 5 ≤ 3 − x.

Solution

We start by adding both sides of the inequality by 5

3x – 5 + 5 ≤ 3 + 5 − x

3x ≤ 8 – x

Then add both sides by x.

3x + x ≤ 8 – x + x

4x ≤ 8

Finally, divide both sides of the inequality by 4 to get;

x ≤ 2

Example 2

Calculate the range of values of y, which satisfies the inequality: y − 4 < 2y + 5.

Solution

Add both sides of the inequality by 4.

y – 4 + 4 < 2y + 5 + 4

y < 2y + 9

Subtract both sides by 2y.

y – 2y < 2y – 2y + 9

Y < 9 Multiply both sides of the inequality by −1 and change the inequality symbol’s direction. y > − 9

Solving linear inequalities with subtraction

Let’s see a few examples below to understand this concept.

Example 3

Solve x + 8 > 5.

Solution

Isolate the variable x by subtracting 8 from both sides of the inequality.

x + 8 – 8 > 5 – 8 => x > −3

Therefore, x > −3.

Example 4

Solve 5x + 10 > 3x + 24.

Solution

Subtract 10 from both sides of the inequality.

5x + 10 – 10 > 3x + 24 – 10

5x > 3x + 14.

Now we subtract both sides of the inequality by 3x.

5x – 3x > 3x – 3x + 14

2x > 14

x > 7

Solving linear inequalities with multiplication

Let’s see a few examples below to understand this concept.

Example 5

Solve x/4 > 5

Solution:

Multiply both sides of an inequality by the denominator of the fraction

4(x/4) > 5 x 4

x > 20

Step-by-step explanation:

Hope this helps :3

Answer:

x=66 and y=63

Step-by-step explanation:

The middle triangle is isosceles

57+57+x=180

114+x=180

x=66

Left triangle is equilateral (all angles =60)

60+57+?=180

117+?=180

?=63

Right triangle is isosceles

?=y

y=63

Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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Answer:

12,500 is 100%, or 1 in decimal terms. We calculate 5% by multiplying 12500 by 0.05.

This gives us a total of £625

Step-by-step explanation:

Brainliest pls

Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right

Step-by-step explanation:

Substitute x for an easy number like 2 and solve.

x - 2/3 - 1/2x = 1/2x - 2/3

x - 1/2 - 3/4x = 1/4x- 1/2

1/3x - 3/4 - 2/3x = -1/3x - 3/4

The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:

Let P(n) be a statement involving an integer n

Base Case: P(m) is true for some m

Induction Hypothesis: Assume P(k) is true for some k>m.

Induction Step: Show that P(k+1) is true.

Therefore, P(n) is true for all n>m

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The exponential equation represents a growth, and the rate of increase is 9%.

The general exponential equation is written as:

y = A*(1 + r)^x

Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).

Here we have:

y = 38*(1.09)^x

We can rewrite this as:

y = 38*(1 + 0.09)^x

So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:

100%*0.09 = 9%

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The larger angle of the right triangle is 139 degrees.

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides.

The three sides of the right triangle are related to each other. This relationship is explained by Pythagoras theorem

In a right triangle, one of the angles is 90 degrees. Let x be the measure of the other acute angle. Then we have:

sin x = cos (90° - x)

We can use this identity to rewrite the given equation as:

sin (9x - 4)° = sin (90° - (10x - 1)°)

Using the identity sin (90° - θ) = cos θ, we can simplify this equation to:

sin (9x - 4)° = cos (10x - 1)°

sin (9x - 4)° = sin ((90°) - (10x - 1)°)

sin (9x - 4)° = sin (10x - 91)°

Since sin θ = sin (180° - θ), we have:

9x - 4 = 180° - (10x - 91)°

9x - 4 = 271° - 10x

Simplifying and solving for x, we get:

19x = 275

x = 275/19

Now, the larger angle of the right triangle is either 9x - 4 or 10x - 1, depending on which is larger. We can calculate both angles and compare them:

9x - 4 = 9(275/19) - 4 = 121°

10x - 1 = 10(275/19) - 1 = 139°

Therefore, the larger angle of the right triangle is 139 degrees.

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The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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Answer:

B.......................

Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

Answer:

3x + 4 < 13

2y - 5 > 7

6n - 1 ≤ 23

8m + 2 ≥ 18

4a - 7 < 5a + 2

9b + 3 > 6b + 10

Step-by-step explanation:

I dunno if this is what you're asking for

Answer:

ok.....

x + 2 < 5

|x - 4| > 4

x + 7 [tex]\geq[/tex] 8

-x < -5

x - 5 < 9

5x + 18 > 2

|3x - 1| < 8

Answer:

20.8

Step-by-step explanation:

Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:

tan(69) = h/8

Multiplying both sides by 8, we get:

8*tan(69) = h

Using a calculator, we get:

h ≈ 20.8 ft

Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.

The radius of the circle with given circumference is 13.

What is circumference?

In mathematics, the circumference of any shape determines the path or boundary that surrounds it. In other words, the perimeter, also referred to as the circumference, helps determine how lengthy the outline of a shape is.

We are given that the circumference of a circle is 81.64 miles.

We know that circumference of a circle is given by 2πr.

So, using this we get

⇒ C  = 2πr

⇒ 81.64  = 2 * 3.14 * r

⇒ 81.64  = 6.28 * r

⇒ r  = 13

Hence, the radius of the circle with given circumference is 13.

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let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]

Answer:

Step-by-step explanation:

modal weight:  the weight that appear most often

4.5 kg  appears 3 times

6-sided polygon:  even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720

therefore, angle f = 720 - 576 = 144      (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)

modal score:  read this right off the graph.  The score with the highest frequency is the modal score:  14   (meaning, 9 contestants got this score)

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Each classroom has 6 rows of 5 desks.

So the total number of desks in one classroom.

= 6 rows x 5 desks per row

= 30 desks

To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.

= 30 desks per classroom x 45 classrooms

= 1,350 desks

Therefore,

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

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The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.

Simple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.

In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:

M = C * (1 + i * t)

3C = C * (1 + 0.04t)

3 = 1 + 0.04t

0.04t = 3 - 1

0.04t = 2

t = 2/0.04

t = 50

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.

It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.

Here we have

The cumulative area is 0.3897

Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:

1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.

2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.

3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.

Therefore,

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

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