What is the answer to -4/5 - 2/3 ?

The object falls from 115200 ft above the ground.

What is the quadratic equation?

A quadratic equation is any algebraic equation of the highest degree. The standard form of the quadratic equation in a variable is ax² + bx + c = 0, where a and b are coefficients, are constant, and is a non-zero numbers.

The acceleration of the object is given by the equation a = 32 - (v^2)/8 ft/s^2. Since the object is initially at rest, we can assume that v = 0 at the start of its fall.

To find the height from which the object fell, we need to use the equations of motion for uniformly accelerated motion. The equation for the distance traveled by an object under constant acceleration is:

d = 1/2 at^2 + vt + d0

where d is the distance traveled, a is the acceleration, t is the time, and d0 is the initial distance (which is zero in this case, since the object is initially at rest).

We know that the object is falling for one minute, and we can convert that to seconds by multiplying by 60. The acceleration is given by a = 32 - (v^2)/8, we know that v = 0, so a = 32 - (0^2)/8 = 32 ft/s^2.

Plugging in the values, we get:

d = 1/2 (32 ft/s^2) (60 s)^2

d = 32 x (3600)

d = 115,200 ft

This is the distance that the object fell. To find the height from which it fell, we simply have to take the distance and negate it.

So the height from which the object fell is:

-115,200 ft

Hence, the object falls from 115200 ft above the ground.

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The expression in the form of q(x) + r(x) / b(x) is

(x + 2) + (-13x + 4) / (x² + 2x + 1).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x³ - 8x + 6) ÷ (x² + 2x + 1)

Using the long division.

x² + 2x + 1 ) x³ - 8x + 6 ( x + 2

                   x³ + 2x² + x

              (-)     (-)        (-)

                      2x² - 9x + 6

                      2x² + 4x + 2

                     (-)    (-)      (-)

                               -13x + 4

Quotient = x + 2

Remainder = -13x + 4

Thus,

Quotient + Remainder / Divisor

= (x + 2) + (-13x + 4) / (x² + 2x + 1).

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The relations in this problem are classified as functions or not as follows:

1. Not a function.

2. Function.

3. Not a function.

4. Function.

5. Function.

A relation represents a function if each value of the input is mapped to only one value of the output.

Hence, a graph will represent a function if, and only if, it contains no vertically aligned points, that is, if there isn't a vertical line that will cross the graph of the relation in more than one point.

Then the graphs that are not functions in this problem are given as follows:

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The surface area of a snowball decreases at a rate of 6 cm²/min. Its diameter decreases at rate of 0.119 cm/minute

The surface area of a ball is given by:

A = 4πr²

  = πd²

Where:

A = surface area

r = radius of the ball

d = diameter of the ball

When the surface area decreases, so does the diameter.

To find the rate of change, take the derivative with respect to time (t)

A =  πd²

dA/dt = 2πd dd/dt

Substitute dA/dt = 6 cm²/min, d = 8 cm:

6 = 2π x 8 dd/dt

dd/dt = 0.119 cm/minute

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Answer: The solution to the system of equations is x = -5 and y = 0.

Step-by-step explanation:

To solve this system of equations by substitution, you can start by solving one of the equations for one of the variables. For example, you can solve the first equation for x:

x + 2y = -5

x = -5 - 2y

Then, you can substitute this expression for x into the second equation to solve for y:

-(-5 - 2y) - 2y = 5

5 + 2y - 2y = 5

5 = 5

Now that you have solved for y, you can substitute this value back into one of the original equations to solve for x. If you substitute y = 0 back into the first equation, you get:

x + 2(0) = -5

x = -5

So, the solution to the system of equations is x = -5 and y = 0.

The congruent angles are - ∠GHF ~ ∠KHJ, ∠GFH ~ ∠KJH and ∠FGH ~ ∠JKH.

The proportion that relates corresponding sides are -

HG/HK = GF/JK = HF/HJ

What is congruency?

Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent.

It is given that ΔFGH is congruent to ΔJKH.

If two triangles are similar.

Then it is known that -

HG/HK = GF/JK = HF/HJ

And all the corresponding angles are equal.

Angles that are congruent to each other is -

Angle GHF ~ KHJ as they are vertically opposite angles.

Angle GFH ~ KJH as they are corresponding angles.

Angle FGH ~ JKH as they are corresponding angles.

The sides which are corresponding and equal are -

HG/HK = GF/JK = HF/HJ

So, GF = JK

GH = HK

FH = HJ

Therefore, all the corresponding angles and sides are listed.

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The height of the zip line is 203 feet.

Trigonometric functions are required when the value of an unknown side or internal angle of a right triangle are to be determined. Some of the basic functions are: sine, cosine, tangent etc.

Tangent of an angle is the ration of the opposite side to the angle and the adjacent side.

Tan θ = opposite/ adjacent

To determine the height of the zip line required in the question, we have;

let the height be represented by h,

Tan θ = opposite/ adjacent

Tan 10 = h/ 1150

h = Tan 10 * 1150

  = 0.1763*1150

  = 202.745

h = 202.8 feet

The height of the zip line is 203 feet.

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The measure of each side of the smaller octagon is 9cm. Therefore, Enter 9

Given that:

The ratio of the sides of two similar regular octagons is 3:11.

The measure of each side of the larger octagon is 33

The measure of each side of the smaller octagon is Ci

we can write that:

smaller octagon : larger octagon  = 3 : 11

smaller octagon / larger octagon  = 3 / 11

smaller octagon / 33  = 3 / 11

smaller octagon = (3 × 33)/11 = 99/11 =  9 cm

Thus, Ci =  9 cm

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Answer:

We can decide algebraically if a function is even, odd or neither by replacing x by -x and computing f(-x). If f(-x) = f(x), the function is even. If f(-x) = -f(x), the function is odd.

Step-by-step explanation:

Answer: m (slope) = 0

Step-by-step explanation:

The slope can be found through the equation (y2-y1)/(x2-x1)

(-4, -9) and (4, -9) can be: (x1, y1) and (x2, y2)

We can plug the variables into the formula above:

(-9-(-9))/(4-(-4) = 0/8

The slope is 0.

Answer: slope=0

Step-by-step explanation:

usually slopes are found by taking

change in y

-----------------

change in x

but in all horizontal lines (matching y values, -9 in this case) the line has no slope as it doesn't go up or down.

Total comparisons required to order an array of 5 elements using the selection sort =29

Selection sort finds the smallest element and swaps it into the first position. The, from the remaining N-1 elements after the first one (which we know is the smallest), it finds the next smallest and swaps it into the 2nd position. And so on.

To find the smallest element from a group of N elements takes N-1 comparisons. Basically, compare item 1 to 2, remember the smallest. Compare item 3 to smallest and remember which ever is smaller, and so on. You end up doing 1 comparison for every element from 2 through N.

We have to find the smallest element N-1 times*, but each time we have a smaller list to look through.

So let’s turn to an array of 5 elements. To find the smallest element will take4 comparisons. Next time through we do 3 comparisons and so on:

Total comparisons = 4+3+2+1 = 10

For N elements it takes 1+2+3+…+N-1 = (N-1)N/2 comparisons.

You don’t have to run through an Nth time because after sorting N-1 items, the Nth item must be in the correct position already. Or, if you like, the Nth loop does N-N=0 comparisons so we can ignore it.

only counting comparisons of elements in the array. A loop is going to have to do a comparison of the loop variable to the length of the array every time it repeats. Usually those comparisons are disregarded because, unless the elements of the array are integers, the item comparisons take considerably more time than the index comparisons, and any way, it won’t increase the asymptotic complexity, only the constant of proportionality. If you want to count the index comparisons, you have one for every item comparison (because the inner loop does one item comparison per loop iteration) + 1 for each end of the inner loop (a loop that runs X times does X+1 comparisons) and then another N-1 for the outer loop + 1 for the loop end. For N = 5 there will be 10 + 4 + 4 + 1 = 19 index comparisons and 10 + 19 = 29 total comparisons.

total comparisons required to order an array of 5 elements using the selection sort =29

of course, if you write this in a language like java that does array bounds checking, you’ll add two more comparisons for each array access. And the compare function is probably a function call, so you’re increasing stack depth which potentially adds comparisons to make sure that doesn’t overflow… you know what? I think I’ll just stop there.

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Answer:

See the explanation below.

Step-by-step explanation:

17) 40=x+45

x = -5

18) 70 = -2 + 8x

72 = 8x

x = 9

19) 19x - 3 = 17x + 11

2x = 14

x = 7

20) -2 + 14x = 12x + 14

2x = 16

x = 8

21) 11x - 3 + 18x + 9 = 180

29x + 6 = 180

29x = 174

x = 6

22) 6x - 4 + 14x + 4 = 180

20x = 180

x = 9

23) 68 + x + x + 128 = 180

196 + 2x = 180

2x = -16

x = -8

24) x + 87 + x + 107 = 180

2x + 194 = 180

2x = -14

x = -7

25) 70 + 12x - 10 = 180

60 + 12x = 180

12x = 120

x = 10

The sample space for the experiment of spinning a four-part spinner is the set of all possible outcomes of the experiment.

In this case, the sample space would be: s = {q, r, s, t}

This means that the possible outcomes of the experiment are q, r, s, and t. Each of these outcomes is equally likely to occur when the spinner is spun.

Option s = {q, r, r, t} is incorrect because it includes two occurrences of the outcome r, which is not possible in this experiment.

Option s = {r, a, t} is incorrect because it includes the outcome a, which is not part of the sample space.

Option s = {s, q, q} is incorrect because it includes two occurrences of the outcome q, which is not possible in this experiment.

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Answer:

a)  8.4

b)  8.5

c)  The mean and median will be one less (7.4 and 7.5).

Step-by-step explanation:

Given number of boxes in each stack:

To find the mean of the number of boxes in a stack, divide the total number of boxes by the number of stacks:

[tex]\implies \sf Mean=\dfrac{5+7+9+ 11+13+ 10+9+ 8+ 7+5}{10}=\dfrac{84}{10}=8.4[/tex]

The median is the middle value when all data values are placed in order of size.

To find the median of the number of boxes in a stack, first place the numbers in order of size:

As there is an even number of boxes (10), the median is the mean of the two middle values:

[tex]\implies \sf Median=\dfrac{8+9}{2}=\dfrac{17}{2}=8.5[/tex]

If one box is removed from each stack, the total number of boxes is 10 less than before.  Therefore:

[tex]\implies \sf Mean=\dfrac{84-10}{10}=\dfrac{74}{10}=7.4[/tex]

The number of boxes in each stack will be (in order of size):

Therefore, the median is 7.5.

So, if one box is removed from each stack:

The required solution to the given expression is 4x² + 5x - 4y - 3.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

y + 2x - 3 + 4x² + 3x - 5y

We have to determine the solution to the given expression.

As per the question, we have

y + 2x - 3 + 4x² + 3x - 5y

Rearrange the variables in the above expression,

4x² + 2x + 3x + y - 5y - 3

Combine likewise terms in the expression,

4x² + 5x - 4y - 3

Thus, the required solution is 4x² + 5x - 4y - 3.

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The question seems to be incomplete the correct question would be:

Find the solution to the below expression.

y + 2x - 3 + 4x² + 3x - 5y

The graph of g(x) = [tex]-log_{2}(x - 3)[/tex] is in graph attached.

The logarithmic function is a crucial tool for mathematical computations. Scottish mathematician, physicist, and astronomer John Napier made the first formal study of logarithms in the 16th century. Numerous astronomical and scientific calculations requiring large numbers can use it. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship.

Given

F(x) = log₂ x

and graph of equation is given in question,

to plot the graph of g(x) = -log₂(x - 3)

The shape of graph will be same as log₂x but in different quadrant because of negative sign.

The point of function g(x) = -log₂(x - 3)

x = 4, g(x) = 0

x = 19, g(x) = -4

and graph will be parallel to y axis at x = 3,

Hence the graph is in image.

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Answer:

A. The total change in the value on the gift card will be -149$

B. Yes, Arleen has enough to buy a Wheelbarrow for 50$

Step-by-step explanation:

A.

To calculate the total change in value of the gift card we need to sum all expenses.

4 days of rental + cost of the rake = total change in value

(4 * -35$) - 9$ = -149$

B.

If the value of the gift card was 200$, then we have to subtract the expenses from the gift card value and check whether we have enough to buy a Wheelbarrow.

200$ - 149$ = 51$ > 50$

Answer:

4

Step-by-step explanation:

Take any point other than (0,0) that is on the line and put it in the form 7/x and that will give you your constant of proportionality.

For example the point graphed is (1,4)  1 is the x value and 4 is the y value.

4/1 = 4

Answer: 4

Step-by-step explanation:

The constant of proportionality is the slope of a line that goes through the origin.

The slope/constant of proportionality is how much the Y increases every time the X increases by 1. Since your graph has the point (1, 4) labeled, the Y goes up 4 units for every 1 unit the X increases by.

Answer:

[tex]\textsf{19.} \quad \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]

[tex]\textsf{20.} \quad \textsf{Center}: \;\;(-4, 1)[/tex]

[tex]\textsf{21.} \quad \textsf{Major axis}:\;\;4\sqrt{3}[/tex]

[tex]\textsf{22.} \quad \textsf{Minor axis}:\;\;4\sqrt{2}[/tex]

[tex]\textsf{23.} \quad \textsf{Sum of the focal radii}:\;\;4 \sqrt{3}[/tex]

[tex]\textsf{24.} \quad \textsf{Foci}:\;\;(-6, 1)\;\; \textsf{and}\;\;(-2,1)[/tex]

[tex]\begin{aligned}\textsf{25.} \quad &\textsf{Vertices}:\;\;(-4-2\sqrt{3}, 1) \;\; \textsf{and}\;\; (-4+2\sqrt{3}, 1)\\ &\textsf{Co-vertices}:\;\;(-4, 1-2\sqrt{2}) \;\; \textsf{and}\;\; (-4, 1+2\sqrt{2})\end{aligned}[/tex]

[tex]\textsf{26.} \quad \textsf{Eccentricity}\;\;\dfrac{\sqrt{3}}{3}[/tex]

27.  See attachment.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\end{minipage}}[/tex]

Given equation:

[tex]2(x+4)^2+3(y-1)^2=24[/tex]

To write the equation of the ellipse in standard form, divide both sides by 24 so that the right side of the equation is equal to one:

[tex]\implies \dfrac{2(x+4)^2}{24}+\dfrac{3(y-1)^2}{24}=\dfrac{24}{24}[/tex]

[tex]\implies \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]

Therefore:

The center of the ellipse is (h, k).

Therefore, the coordinates of the center are (-4, 1).

As a > b, the ellipse is horizontal, so 2a is the major axis and 2b is the minor axis.  Therefore:

The focal radius is the distance from a point on the ellipse to a focus.

The sum of the focal radii is equal to the length of the major axis.

Therefore, the sum of the focal radii is 4√3.

As a > b, the coordinates of the foci are (h±c, k).

As c² = a² - b², first find the value of c:

[tex]\implies c^2=12-8[/tex]

[tex]\implies c=\sqrt{4}=2[/tex]

Therefore, the coordinates of the foci are:

As a > b, the coordinates of the vertices are (h±a, k):

and the coordinates of the co-vertices are (h, k±b):

The eccentricity of the ellipse is:

[tex]\implies e=\dfrac{c}{a}=\dfrac{2}{2\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]

z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

The ratios of the long leg to hypotenuse are the same for all right triangles since they are similar:

z/7 = 5/z

When z2 equals 35, multiply by 7z.

z = √35

z = √35 is the ratio of the long leg to the hypotenuse and the exact value of z are shown in the diagram below.

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Answer:

Step-by-step explanation:

∠a is opposite to BC. Option D is correct.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is ABC

In the given triangle AB, BC and AC are the edges or sides.

A, B and C are the vertices of triangles.

∠a, ∠b and ∠c are the angles.

In the given triangle we need to find what is opposite to the ∠a

∠a is opposite to the BC

Hence, ∠a is opposite to BC. Option D is correct.

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The value of the variable, S when  C = 6, n = 8, T = 1 and k = 18 is 1. 036

To make a variable the subject of formula, we have to make it stand alone on one end of the equality sign.

From the information given, we have the equation as;

C = n/Tk(1 + S²)

Now, let's cross multiply to make 'S' the subject of formula, we get;

C× Tk(1 + S²) = n

Divide both sides by the coefficient of S

1 + S² = n/CTk

collect '1' to the other side;

S² = n/CTk + 1

Take the square root of both sides

S = [tex]\sqrt{\frac{n}{CTk} + 1 }[/tex]

Now, substitute the values

S = [tex]\sqrt{\frac{8}{6* 1 * 18} + 1 }[/tex]

Multiply the values

S = [tex]\sqrt{1. 074}[/tex]

S = 1. 036

Thus, the value is 1. 036

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The time when the altitude of the balloon is 370.4 feet is 6 minutes.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope the steeper is its graph or the rate of change is large.

We know The slope of the line is (y₂ - y₁)/(x₂ - x₁).

Therefore, The slope of the line passing through the points

​(0​,428​) and ​(10​,​332) is,

Slope(m) = (332 - 428)/(10 - 0).

Slope(m) = - 9.6, So the balloon is descending at a rate of - 9.6 feet per minute.

Now, To obtain the y-intercept.

428 = - 9.6(0) + b.

b = 428.

Therefore, The equation of the required line is,

y = - 9.6x + 428, where y is the altitude and x is the number of minutes.

So, The time in minutes when the altitude of the balloon is 370.4 feet is,

370.4 = - 9.6x + 428.

- 9.6x = - 57.6.

x = 57.6/9.6.

x = 6 minutes.

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The inequality that represents the third side of the given triangle is  3 < x <19.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, The side length of the triangle are 8, 11, and x.

From the General property of the triangle

The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is more than the length of the 1/3 side. In the same way, the difference between the various 2 sides of a triangle is a great deal much less than the length of the 3rd side.  

Since the sum of two sides should be greater than the third

x < 8 + 11

=> x < 19

Since the difference between the two sides of a triangle is less than the length of the third side.

=> x > 11 - 8

=> x > 3

therefore, The inequality that represents the third side of the given triangle is  3 < x <19.

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The slope intercept form for the cost of tickets can be written as  C = 26t + 16.50.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

As per the question, the number of tickets are represented as t and cost as C.

The slope from the table can be found as,

⇒ (68.50 - 42.50) ÷ (2 - 1) = 26

Plug m = 26 in y = mx + c to get,

y = 26x + c

Plug y = 42.50 and x = 1 to get,

⇒ 42.50 = 26 × 1 + c

⇒ c = 16.50

Then, the equation can be written in terms of C and t as,

C = 26t + 16.50

where c = 16.50

Hence, the equation to represent the total cost is given as C = 26t + 16.50.

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The radical would to become -10 -21√x11.

We define the term like radicals as the kind of radicals that have the same kind of values inside the radical sign. This implies that they have similar values in the square root sign. When this is the case, we can be able to handle the radical as an algebraic expression and then simplify it accordingly.

In this case, we would have that;

-10 -10√x11 - 11√x11

-10 -21√x11

This is now the simplified form of the expression that has been shown here.

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The equation of the line through the point (7,8) and (-12, -11) is y = x + 1. Thus, option c is correct.

Linear equations are characterised by variables with a power of one. Where ax+b = 0 is one example with one variable, where a and b are real numbers and x is the variable.

Linear algebra covers a wide range of topics. Applications, abstract, and numerical methods are all part of its range. Numerous other disciplines, including fractal geometry, differential equations, difference equations, relativity, archaeology, and demography, depend on linear algebra.

Using the slope formula, we can find the equation of the line [passing through the point (7,8) and (-12, -11) i.e.

y₂ - y₁ = m(x₂ - x₁)

Putting the values

-11 - 8 = m(-12 - 7)

-19 = m(-19)

m = -19/-19

m = 1

Now, we have slope so find the line

y - 8 = 1(x - 7)

y = x - 7 + 8

y = x + 1

y - (-11)= 1(x - (-12))

y + 11= x  12

y = x + 1

Thus, The equation of the line through the point (7,8) and (-12, -11) is y = x + 1.

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