A whale descends from the surface of the water at a rate of 22 feet per minute.
What is the position of the whale relative to the surface after diving for 3
minutes?

For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .

The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .

The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;

On differentiating both sides of the curve with respect to "x"  ,

we get ;

the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;

Now for the  x- intercepts , the value [tex]y = 0 ,[/tex]

On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,

we get ;

[tex]x^{2} +x(0)+0^{2} =27[/tex]

On simplifying further ,

we get ;

[tex]x=\pm 3\sqrt{3}[/tex] ;

So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;

to find the slopes , we substitute the values in the slope equation .

On substituting the values in the slope equation ,

we get ;

[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex]  and

[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].

we see that the slope at both the intercepts is same ,

Therefore , the lines tangents of the curve at the x intercepts are parallel .

The given question is incomplete , the complete question is

Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .

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Answer:

Ron killed 8 times as many spiders as Harry: R = 8 * H

Step-by-step explanation:

This expression represents the situation in which Ron killed 8 times as many spiders as Harry.

Therefore, the measures of those two angles are 33° and 24°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

We know, the sum of the angles in a triangle is always 180 degrees.

126 + x + y = 180

x + y = 54

Given that the two angles are in a ratio of 11:16, the proportion:

x/y = 11/16

Solving for x and y, we get:

x = 11y/16

We substitute this equation into the equation x + y = 54 and we get:

11y/16 + y = 54

Solving for y we get y = 24. Then we can use the proportion to find x:

x = 11 * 24 / 16 = 33.

So the two angles are 33° and 24°.

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Answer:

Step-by-step explanation:

To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).

Given that the discount is 3% and we want to find the price after the discount, that means:

1 - (3/100) = 1 - 0.03 = 0.97

So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.

For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7

10*0.97 = 9.7

The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

A linear equation (degree 1) has one real solution.

A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.

A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.

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Answer:

Step-by-step explanation:

Answer:

6,532

Step-by-step explanation:

ixl

Answer:

1/100, or 0.01, or 10^-2

Step-by-step explanation:

Simplify to get 1/10^2

and evaluate to get 1/100 or some the alternative forms (see above)

Hassan can paint maximum 11 bookcases with 10 gallons of paint.

A fraction represents a numerical value, which defines the parts of a whole.

Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction.

Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.

Given,

Hassan has 10 gallons of paints.

1 bookcase requires 7/8 gallons of paint

Let Hassan paints x bookcases.

According to the question

7/8x = 10

7x = 80

x = 80/7

x = 11.43

But no. of bookcases should be in whole.

Number of bookcases painted with 10 gallons of paint = 11.

Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint

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Answer:

2/15

Step-by-step explanation:

make x= 0.13

multiply it by  10^1 .  

10x = − 1.33

subtract x from 10x

10x−x =

1.33 - 0.13

9x =  1.2  

divide both sides by 9 to get x as a fraction

x =  1.2/9  =  

12/90  =  

2/15

httpssocraticorgquestionshowdoyouconvert0133beingrepeatedtoafraction#242780

A bar over a digit in a decimal number, such as 0.133 with a bar over the 3, indicates that the number is a repeating decimal. In this case, 0.133 is a repeating decimal and the digit 3 is repeating infinitely.

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The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).

Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:

y = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:

y = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)

f(x) = (x + 7) · (x - 3) · (x - r)

Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.

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Answer:

I think you do know how because where the point is now is correct!!

The solution to the system of equations is x = 3 and y = 4.

this question is related to system of equations ,

the equations are,

x + y = 7         .......[1]

x + 2y = 11  

x= 11 - 2y

now, place the value of x in equation 1,

(11 - 2y) + y = 7

11 - 2y +y = 7

11 - y = 7

- y = 7 - 11

- y = - 4

y = 4

now to find the value of x, place the value of y in equation 1

x + 4 = 7

x = 7 - 4

x = 3.

so, the value of x and y is 3 and 4.

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Step-by-step explanation:

x² - 32 = 4x

x² - 4x - 32 = 0

with a little bit experience we see immediately that this is

(x - 8)(x + 4) = 0

the positive x for this to be true is x = 8.

formally, the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =

= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =

= (4 ± 12)/2 = 2 ± 6

x1 = 2 + 6 = 8

x2 = 2 - 6 = -4

we were right at the beginning.

the positive solution is x = 8.

Answer:

see explanation

Step-by-step explanation:

A

for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.

In this case we are only given 1 pair of congruent angles.

Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.

B

the sides are of different lengths but the ratios of corresponding sides are equal, that is

[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2

If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so

Δ GHI and Δ JKL are similar by the SAS postulate

C

the ratios of corresponding sides are equal , then

[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]

[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

KL = 14

If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.

6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

The given quadratic expression 12x^2+x-20

now, 12x^2 + 16x - 15x - 20

4x (3x+4) - 5(3x+4)

(4x-5) (3x+4)

the root of the equation is (4x-5) (3x+4)

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To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let's begin with a straightforward equation: x + 2 = 7.

How do you obtain X on your own?

Take away two from both sides.

⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5

Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.

R.H.S. L.H.S.

Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.

With the aid of an example, let's clarify how to solve for x in a triangle.

Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.

By using the Pythagorean theorem to ABC,

We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.

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Answer:

Yes

Step-by-step explanation:

y = x has the inverse x = y

By solving the equation 5t - 3 = 3t - 5 we get the equation is true when t = -1. So the solution is t = -1.

To solve the equation 5t - 3 = 3t - 5, you can use algebraic manipulation to isolate the variable on one side of the equation.

The first step is to get all the terms with the variable on one side of the equation and all the constant terms on the other side.

5t - 3 = 3t - 5

adding 3 to both sides:

5t = 3t - 2

subtracting 3t from both sides:

2t = -2

then divide both sides by 2:

t = -1

So the solution is t = -1, meaning that when t = -1, the equation is true.

--The question is not clear, answering to the question below--

"How do you solve the equation 5t - 3 = 3t - 5?"

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log 30+ log 6 is not equivalent to log 36

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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Answer: 1.

Step-by-step explanation:

[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.

The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.

Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.

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Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Here,

Given : The parallelogram  has M angle  =100 degree

And to Find :L angle

In a parallelogram sum of the adjacent angle is 180°, So

So ,

Using this parallelogram property ,

we find :

=>100 + L =180

=> L = 80

Thus,

We get the L value using parallelogram properties.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

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The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Three shapes—a rectangle, a triangle, and a semicircle—make up the figure.

Triangle + rectangle + semicircle together make up the figure's surface area.

Triangle's area is equal to 1/2 * 3 * 5.

Triangle's surface area is 15/2.

Triangle's surface area is 7.5 m3.

Rectangle area equals length times width

Rectangle's area is equal to 6 x 5.

30 m2 is the rectangle's area.

Semicircle area equals πr²/2

Semicircle's area is equal to π(3)²/2

Semicircle's area is equal to 3.14(9)/2.

Semicircle's area is equal to 3.14 x 4.5.

Semicircle's surface area is 14.13 m2.

Area: 30 + 14.13 + 7.5

The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.

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Answer: D

Step-by-step explanation:

Since we are given 2 points, we can use that to find slope, convert to slope-intercept form, and then manipulate it to be standard form. Standard form is ax+by=c.

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-8}{1-(-9)} =\frac{-20}{10} =-2[/tex]

With m=-2, we can plug it into slope-intercept form to find the y-intercept.

[tex]y=-2x+b[/tex]         [plug in point]

[tex]8=-2(-9)+b[/tex]    [multiply]

[tex]8=18+b[/tex]             [subtract both sides by 18]

[tex]b=-10[/tex]

With m and b, we can plug in the equation.

[tex]y=-2x-10[/tex]        [add both sides by 2x]

[tex]2x+y=-10[/tex]

This gives D as the answer.

The probability that Sabreena is going to lose is given as 0.5833

Probability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.

A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.

If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7

In this case, the odds of Sabreena winning are 5:7,

so the probability of winning is 5/(5+7)

the probability of not winning is 1 -  5/12

The probability of not winning is approximately 0.5833

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The length of the side of the table top as calculated from the given data will be 6x⁴y².

To calculate the area of the table top we will have to square of the sides given .

area =(36x.16y^4 )²

side =√(36x.16y^4 )²

= 6x⁴y².

In mathematics the product of a number multiplied by itself is considered to be its square. Eg.) 6 multiplied by 6 gives 36 which is known as its square.

The given table is square in shape and hence its area will be given my multiplying its side with itself.

Area of a square = side x side.

To find its length we can simply find the square root of the number.

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This situation can be represented with an equation as y = mx + b. The constant of proportionality (m) is a number that represents how much flour is needed for each additional batch of cookies. If the equation is in the form y = mx + b, then the relationship is proportional.

Shiloh needs to make multiple batches of cookies from a recipe that calls for 2 2/3 cups of flour to make two regular batches. To represent this situation in an equation, the equation is y = mx + b, where y is the amount of flour needed for the number of batches (x) Shiloh is making, m is the constant of proportionality, and b is the initial amount of flour needed (2 2/3 cups).

The constant of proportionality (m) in the situation above is the measure of how much flour is needed for each additional batch of cookies. For example, if the constant of proportionality is 0.75, that means Shiloh would need to add 0.75 cups of flour for each additional batch of cookies.

Therefore, if Shiloh is making three batches of cookies, the equation would be y = 0.75x + 2 2/3, and the total amount of flour needed would be 4 1/8 cups (2 2/3 + 0.75 + 0.75).

By using an equation to represent this situation, it is easy to determine if a relationship is proportional.

If the equation is in the form y = mx + b, then the relationship is proportional.

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