The equation of a line is given by 3x +4y =12. Solve for y.

    |<---- 20 cm ---->|

    |                  |  

    +------------------+  

    |<---- 41 cm ---->|

    |                  |  

    +------------------+  

    |<---- 44 cm ---->|

    |                  |  

    +------------------+

After x is cut off each rod, the remaining lengths can be arranged to form a right triangle, as shown below:

               +---------(44-x)--------+

               |                        |

               |                        |

               |                        |

               |                        |

               |                        |

               |                        |

   (20-x)      |                        |     (41-x)

   +-----------+------------------------+

               |         x              |

b) To model the situation, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:

(20-x)^2 + (41-x)^2 = (44-x)^2

c) To find the length that is cut off, we can solve the equation from part (b) for x. First, we can simplify the equation by expanding the squares:

400 - 40x + x^2 + 1681 - 82x + x^2 = 1936 - 88x + x^2

Simplifying further, we get:

2x^2 - 18x - 855 = 0

We can solve for x by using the quadratic formula:

x = [18 ± sqrt(18^2 + 4(2)(855))] / (2(2))

x = [18 ± sqrt(7404)] / 4

x ≈ 16.98 or x ≈ -24.98

Since x represents a length that is cut off each rod, it must be positive. Therefore, we can discard the negative solution and conclude that the length that is cut off is approximately 16.98 cm.

d) Using the length that is cut off, we can find the dimensions of the right triangle by substituting x = 16.98 into the expressions for the remaining lengths. We get:

(20 - 16.98) = 3.02 cm

(41 - 16.98) = 24.02 cm

(44 - 16.98) = 27.02 cm

Therefore, the dimensions of the right triangle are 3.02 cm, 24.02 cm, and 27.02 cm.

The angle Y measures 39 degrees. According to the given question.

How to find angle in triangle ?

To find the measure of an angle in a triangle, you need to know the measures of the other two angles in the triangle. Since the sum of all angles in a triangle is always 180 degrees, you can use this fact to calculate the measure of the third angle.

There are a few different methods we can use to find the measure of an angle in a triangle:

Subtract the measures of the other two angles from 180 degrees. This works for any triangle, regardless of its shape or size.

Use the fact that the angles opposite equal sides of a triangle are equal. This is known as the "angle-side-angle" (ASA) theorem. For example, if you know the lengths of two sides of a triangle and the angle between them, you can use the Law of Cosines to find the third side and then use the Law of Sines to find the opposite angle.

Use the fact that the angles in a right triangle are related by the Pythagorean Theorem. If you know the lengths of two sides of a right triangle, you can use the Pythagorean Theorem to find the length of the third side, and then use trigonometric ratios (sine, cosine, tangent) to find the measure of the angle opposite the known side.

Use the fact that the angles in an equilateral triangle are all equal. If you know that a triangle is equilateral, you can simply divide 180 degrees by 3 to find the measure of each angle.

In a triangle, the sum of all angles is always 180 degrees. Therefore, we can use this fact to find the measure of angle Y:

angle Z + angle X + angle Y = 180 degrees

Substituting the given values:

113 degrees + 28 degrees + angle Y = 180 degrees

Simplifying and solving for angle Y:

141 degrees + angle Y = 180 degrees

angle Y = 180 degrees - 141 degrees

angle Y = 39 degrees

Therefore, angle Y measures 39 degrees.

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Your complete question is :-ALGEBRA In Triangle XYZ, angle  Z=113 and angle X=28°. What is angle Y?

As a result, when the camera and the rocket are 4255 feet apart, the rate  trigonometry of change in the angle of elevation after launch is roughly -0.15807 radians/foot.

Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.

Where is the camera's angle of elevation and c is the rocket's height above ground level.

We may express the angle of elevation using the given formula as:

r θ = tan⁻¹(c/2000)

c2 + x2 = d2, where d = 4255 ft 2c(dc/dx) + 2x = 0, and dc/dx = -x/c.

When we multiply c by 2000 tan() and x by (d2 - 20002) (since x is the horizontal distance between the camera and the rocket), we get: dc/dx = -(d2 - 20002) / (2000 tan())

tan1(0.02d/2000) = tan1(d/100000)

dc/dx = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -0.005(d2 - 20002) / d

dc/dx = -0.005(42552 - 20002) / 4255 -0.15807 radians per foot

As a result, when the camera and the rocket are 4255 feet apart, the rate of change in the angle of elevation after launch is roughly -0.15807 radians/foot.

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Using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².

A patch's area on a surface determines how big it is.

Whereas a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

A plane figure's area is the space that its perimeter encompasses.

The area of a closed figure is the total number of unit squares covering its surface.

The area is measured in square units like cm² and m².

So, we know that the area of the triangle is now:

A = 1/2s²

The side of the square is: 10 cm

Then, the area of the one triangle is:

A = 1/2s²

A = 1/2*10²

A = 1/2*100

A = 50 cm²

Therefore, using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².

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Step-by-step explanation:

it is 8 bcs -1 - 3 = -4 turn it to 4 and +4

Considering the expression of a line, an equation for the line best fit to the points (0, 60) and (4, 90) is y=7.5x +60.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂), the slope m can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

In this case, being (x₁, y₁)= (0, 60) and (x₂, y₂)= (4, 90), the slope can be calculated as:

m= (90 - 60)÷ (4-0)

m= 30÷ 4

m= 7.5

Considering point 1 and the slope m, you obtain:

60= 7.5×0 + b

60= 0 +b

60= b

Finally, the equation of the line is y=7.5x +60.

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Answer:

(12, 15)

Step-by-step explanation:

Proofs attached to answer

Answer: Let's begin by assigning variables to represent the dimensions of the room. Let's use "l" to represent the length and "w" to represent the width.

We know that the length of the room is 5 feet longer than twice the width, so we can write an equation:

l = 2w + 5

We also know that the perimeter of the room is 178 feet. The formula for the perimeter of a rectangle is:

perimeter = 2(length + width)

Substituting the equation we found for the length, we get:

178 = 2(2w+5 + w)

Simplifying, we can combine like terms and solve for w:

178 = 2(3w+5)

89 = 3w+5

84 = 3w

w = 28

Now that we know the width is 28 feet, we can use the equation for the length to find the length:

l = 2w+5 = 2(28)+5 = 61

Therefore, the dimensions of the room are 61 feet by 28 feet.

Step-by-step explanation:

AB can be identified to be, based on the circle, to be a A. Major arc.

The measure of the arc would be 226 degrees.

A major arc is an arc on a circle that is greater than 180 degrees, or half the circumference of the circle. A major arc is also known as a large arc. It extends from one endpoint of a minor arc to the other endpoint of the same arc, passing through the center of the circle.

AB is a major arc because it is larger than half of the circle which means it is greater than 180s degrees.

The measure of arc AB is:

= Half a circle angle + arc CB

= 180 + 46

= 226 degrees

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[tex]\textit{Pythagorean Identities} \\\\ 1+\tan^2(\theta)=\sec^2(\theta)\implies \tan^2(\theta)=\sec^2(\theta)-1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{ \textit{difference of squares} }{[sec(x)+1][sec(x)-1]}}{sin^2(x)}\implies \cfrac{sec(x)^2-1^2}{sin^2(x)}\implies \cfrac{sec(x)^2-1}{sin^2(x)} \\\\\\ \cfrac{tan^2(x)}{sin^2(x)}\implies \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{1}{cos^2(x)}\implies sec^2(x)[/tex]

Answer:

Its both box A and B, Answer D

Step-by-step explanation:

Box A has a volume of 14

Box B has a volume of 15

Answer:

D. Both box A and box B

Hope this helps!

Step-by-step explanation:

Volume = L * W * H

The pillows have a volume of 13.5

Box A has a volume of 14

Box B has a volume of 15

Both boxes can hold the pillows.

The length and width οf the rectangle are 11 inches and 4 inches, respectively.

Area οf rectangle can be defined as prοduct οf length , breadth οf a rectangle.

Let's denοte the width οf the rectangle as w. Then accοrding tο the prοblem, the length οf the rectangle is 7 inches mοre than the width, sο we can express the length as w + 7.

The area οf the rectangle is given by:

[tex]A = length * width = (w + 7) * w = w^2 + 7w[/tex]

The perimeter οf the rectangle is given by:

[tex]P = 2 * (length + width) = 2 * (w + 7 + w) = 4w + 14[/tex]

According tο the problem, the area of the rectangle is equal to 2 inches mοre than 2 times the perimeter, so we can set up the following equation:

[tex]w^2 + 7w = 2(4w + 14) + 2[/tex]

Simplifying this equatiοn, we get:

[tex]w^2 + 7w = 8w + 28[/tex]

Subtracting 8w + 28 frοm both sides, we get:

[tex]w^2 - w - 28 = 0[/tex]

We can factοr this quadratic equation as:

[tex](w - 4)(w + 7) = 0[/tex]

Therefοre, we have twο sοlutiοns fοr w: w = 4 and w = -7. Hοwever, since the width οf the rectangle cannοt be negative, we reject the sοlutiοn w = -7 and chοοse w = 4 as the width οf the rectangle.

Then, the length οf the rectangle is w + 7 = 4 + 7 = 11 inches.

Therefοre, the length and width οf the rectangle are 11 inches and 4 inches, respectively.

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Answer:

a^2=9

Step-by-step explanation:

there is a rule that states that if you multiply - with - it becomes + so a number squared just means that the number multiplies with itself so -3*-3=+9 or 9 (any number with + can be written as the number without the +sign, for ex. +1 is the same as 1)

Answer:

the average velocity of the ball on the interval [1, 3/2] is -808 ft/s.

Step-by-step explanation:

The height of the ball at time t is given by the formula:

s(t) = -16t^2 + 50t + 1200

We need to find the average velocity of the ball on the interval [1, 3/2]. The average velocity is defined as the change in position divided by the change in time, or:

average velocity = (s(3/2) - s(1)) / (3/2 - 1)

Substituting the formula for s(t), we get:

average velocity = ((-16(3/2)^2 + 50(3/2) + 1200) - (-16(1)^2 + 50(1) + 1200)) / (3/2 - 1)

Simplifying and solving for the average velocity, we get:

average velocity = (430 - 1234) / (1/2) = -808 ft/s

Therefore, the average velocity of the ball on the interval [1, 3/2] is -808 ft/s.

274.75 square inches of pizza are remaining. Option A is the correct option.

What is π in math?

The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.

Given that, the diameter of large pizza is 20 inches.

The radius of a circular shape is half of the diameter.

The radius of the pizza is (20 inches)/2 = 10 inches.

Area of a circular shape is ∏r² .

The area of the pizza is 3.14×10² = 314 in²

The total part of the pizza is considered as 1.

One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.

The area of remaining pizza is

314 in²  × (7/8)

= 274.75 square inches

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If Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him.

a) The guitar to a convenient amount is $180.

b) 10% of the rounded price is $18.

c) 1% of the rounded price is $1.80

d) 13 1%s is needed

e) The estimated tax is $23.40

f)The  estimated tax to the rounded price is $203.40.

g) No Kareem does not enough money with him.

a) Let's round the price of the guitar to the nearest dollar for convenience. $179.99 rounds up to $180.

b) 10% of $180:

$180× 10% =$18

c) 1% of $180:

180× 1% =  $1.80

d) How many 1%s do you need?

To find out how many 1%s we need, we can divide the estimated tax rate of 13% by 1%:

13 ÷ 1 = 13

So we need 13 1%s.

e) To find the estimated tax, we can multiply the rounded price by the tax rate of 13%:

$180 x 0.13 = $23.40

f) Add the estimated tax to the rounded price:

$180 + $23.40 = $203.40

Since Kareem has $200 cash with him, he does not have enough money to buy the guitar. Therefore, the answer is NO, he does not have enough money.

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The solution of the given problem of arithmetic mean comes out to be  given series is therefore a geometric sequence.

A list's values are added up to get the average values, also known as the company's means, which is then multiplied by the maximum population of list elements. Similar development patterns can be seen in math. The median of the actual numbers 5, 8, and 9 is 3, while for mean of the real figures 5, 7, as well as 9 is 4, and the number 21 increased by three (there are currently several three numbers) = seven. This is demonstrated by the following equation.

Here,

It is a geometric sequence that is provided.

A mathematical sequence known as a geometric sequence is one in which each term following the first is obtained by multiplying the preceding term by a fixed ratio known as the common ratio. A geometric sequence's overall formula is

=>  a = a1 + [tex]r^{(n-1)[/tex] (n-1)

where r is the common ratio, n is the amount of terms, and an is the nth term. A1 is the first term.

The first word in the listed order is:

=> a1 = 1/2(4)⁰ = 1/2

Any term can be divided by the preceding term to find the common ratio:

=>  a2/a1 = (1/2(4)¹)/(1/2(4)⁰) = 4/2 = 2

=>  a3/a2 = (1/2(4)²)/(1/2(4)¹) = 4/2 = 2

so forth.

This series is a geometric sequence because the common ratio is constant.

The given series is therefore a geometric sequence.

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Complete question:

Identify the following as arithmetic or geometric,

aⁿ = ½(4)n-1

By derivative rules we find the following conclusions from functions:

In this question we find two cases where the second derivative of a function must be found, this can be done by applying derivative rules twice. The first case consists in determining the second derivative of the following function:

y = 3 / x - 7 · ㏑ x

First derivative

y' = - 3 / x² - 7 / x

Second derivative

y'' = 6 / x³ + 7 / x²

The second case requires the determination and evaluation of the second derivative of the following function:

s = 2 / t - 2 / t², t = 2

First derivative

s' = - 2 / t² + 4 / t³

Second derivative

s'' = 4 / t³ - 12 / t⁴

Evaluation

s'' = 4 / 2³ - 12 / 2⁴

s'' = 1 / 2 - 3 / 4

s'' = - 1 / 4 ft / sec²

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The length would initially decrease to AB - BC before increasing to a maximum of AB + BC.

We can see from the diagram that two triangles are generated when AB = 3 cm and BC = 1.5 cm.

This would occur if, at point AC, C were to be rotating counterclockwise around A.

As AC moves closer to A, AC will initially decline to AB - BC. It would then grow. The length would be AB + BC at its greatest.

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The odds in favor of drawing a 7 are 1 to 12.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are four 7s in a deck of 52 cards, so the probability of drawing a 7 is 4/52, which simplifies to 1/13. The odds in favor of drawing a 7 are the ratio of the probability of drawing a 7 to the probability of not drawing a 7, which is:

(1/13) : (12/13

We can simplify this ratio by dividing both terms by the greatest common factor, which is 1:

(1/13) : (12/13) = 1 : 12

Therefore, the odds in favor of drawing a 7 are 1 to 12.

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Therefore , the solution of the given problem of equation comes out to be n = 3.

The same variable word is frequently used in mathematical formulas to attempt to ensure consistency between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Instead of dividing 12 into two portions in this instance, the normalise function adds b + 6 to use the illustration of

y + 6.

Here,

Part 1: We will add 1 to both sides of the equation because we want to separate n in this situation:

=> n - 1 + 1 = 2 + 1

Simplifying:

=> n = 3

Consequently, n = 3 is the answer to the problem n - 1 = 2 when n is taken into account.

To put it up:

=> n - 1 = 2

To both ends, add one:

=> n - 1 + 1 = 2 + 1

Simplify:

=>n = 3

Part 2:

In order to isolate the variable (n) on one side of the equation, we can use inverse operations to answer for n in the equation n - 1 = 2.

Addition is the opposite of reduction. In order to isolate n in this example, we therefore add 1 to both sides of the equation using the inverse process of subtraction.

The steps required are as follows:

=>  n - 1 = 2 (original calculation) (original equation)

To both ends, add one:

=>  n - 1 + 1 = 2 + 1

Simplify:

=> n = 3

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The quadrilateral in the diagram is a rectangle, which is a special type of parallelogram.

No, a parallelogram does not have equal angles on all sides. The opposite angles of a parallelogram are equal, and the consecutive (adjacent) angles are supplementary, according to two fundamental theorems about parallelograms' angles.

There is a quadrilateral with four sides in the provided diagram. It is a parallelogram because the opposite sides are parallel and congruent, and the opposite angles are congruent.

We can also deduce that it is a rectangle because all angles are right angles (90 degrees).

As a result, the diagram's quadrilateral is a rectangle, a particular kind of parallelogram.

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Answer:

To find the amount of interest earned by depositing $220 into an account that earns 4% interest for one year, we can use the simple interest formula:

Interest = Principal * Rate * Time

Where:

Principal = $220 (the amount deposited)

Rate = 4% (expressed as a decimal, so 0.04)

Time = 1 year

Plugging in these values, we get:

Interest = $220 * 0.04 * 1

Interest = $8.80

Therefore, the amount of interest earned by depositing $220 into an account that earns 4% interest for one year is $8.80.

Answer:

Sandra walked longer by 240 - 230 = 10 meters.

Step-by-step explanation:

To find out who walked longer and by how much, we need to calculate the distance walked by each person.

For Jay who walked two rounds around Ace Park, the distance walked is:

Distance = 2 × (length + width) = 2 × (75 + 40) = 230 meters

For Sandra who walked two rounds around Lewis Park, the distance walked is:

Distance = 2 × (length + width) = 2 × (90 + 30) = 240 meters

Therefore, Sandra walked longer by 240 - 230 = 10 meters.

Answer: 46.39 grams of radium

Step-by-step explanation:

We can use the half-life formula to solve this problem:

A = A₀(1/2)^(t/t₁/₂)

where:

A₀ = initial amount (present)

A = final amount (in 710 years)

t = time elapsed (710 years)

t₁/₂ = half-life (1690 years)

First, we need to calculate the number of half-lives that will occur in 710 years:

n = t / t₁/₂

n = 710 / 1690

n ≈ 0.42

This means that in 710 years, the amount of radium will be reduced to half its current amount (1/2). And then reduced to half again (1/2 * 1/2) in another 1690 years.

Now we can calculate the final amount of radium after 710 years:

A = A₀(1/2)^n

A = 70(1/2)^0.42

A ≈ 46.39 grams

Therefore, after 710 years, approximately 46.39 grams of radium will be left.

(a) The 40% grοwth in decimal is 0.4.

(b)  1st mοnth    2nd mοnth   3rd mοnth      4th mοnth         5th mοnth

       150                   210                294               412                  577

A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, we shοuld divide it by its entirety and then multiply it by 100. The percentage, therefοre, refers tο a part per hundred. Per 100 is what the wοrd percent means. The letter "%" stands fοr it.

The given percentage is 40%.

Cοnvert it fractiοn 40 × 1/100

Cοnvert it decimal fοrm:

= 0.4

First mοnth:

The number οf listeners is 150.

Secοnd mοnth:

The number οf listeners is

150 + (150×0.4)

=150 + 60

= 210

Third mοnth:

The number οf listeners is

210 + (210×0.4)

=210 + 84

= 294

Fοurth mοnth:

The number οf listeners is

294 + (294×0.4)

=294 + 117.6

= 411.6

≈ 412

Fifth mοnth:

The number οf listeners is

412 + (412×0.4)

=412 + 164.8

=  576.8

≈ 577

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Answer:

Lowest possible score is 59.865 and you can still maintain an 80 by the end.

Step-by-step explanation:

The simplified fοrm οf the expressiοn is 1 - cοs2x.

Trigοnοmetry is the branch οf mathematics that studies the relatiοnship between the sides and angles οf a triangle, particularly a right-angled triangle. The relatiοnship is shοwn by the ratiο οf the sides, which are trigοnοmetric ratiοs. There are six ratiοs in trigοnοmetry: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

We can simplify the expressiοn cοs2x−2cοs2x+1 as fοllοws:

cοs2x − 2cοs2x + 1

= (cοs2x - cοs2x) - 2cοs2x + 1 (using the identity cοs2x = cοs2x - cοs2x + 1)

= -cοs2x + 1

= 1 - cοs2x

Therefοre, the simplified fοrm οf the expressiοn is 1 - cοs2x.

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Answer:

Letting x be the missing length, we have

[tex]7 < x < 23[/tex]

Step-by-step explanation:

According to the Triangle Inequality Theorem:

8 + x > 15 -------> x > 7

8 + 15 > x -------> x < 23

x + 15 > 8 -------> x > -7

So we have 7 < x < 23.