two consecutive even numbers whoes sum is 126

Answer:

sin = \(\frac{16}{20}\)

Step-by-step explanation:

given

cos = \(\frac{12}{20}\) = \(\frac{adjacent}{hypotenuse}\)

this is a right triangle with hypotenuse = 20 and adjacent = 12

using Pythagoras' identity to find the side opposite (opp ) , then

opp² + 12² = 20²

opp² + 144 = 400 ( subtract 144 from both sides )

opp² = 256 ( take square root of both sides )

opp = \(\sqrt{256}\) = 16

then

sin = \(\frac{opposite}{hypotenuse}\) = \(\frac{16}{20}\)

The length of side SW is greater than the length of side PW.

Side SW has the shortest length of the three sides.

A triangle is a two-dimensional geometric shape that is defined by three straight sides and three angles. It is the simplest polygon with three sides and three vertices.

We know that the magnitude x is gotten from;

x² - 11x + 146 + 39 - 3x +44 = 180 (Sum of angles in a triangle)

x²- 11x - 3x + 146 + 39  +44 = 180

x²- 14x + 229= 180

x²- 14x = 180 - 229

x²- 14x = -49

Hence;

x²- 14x + 49 = 0

x = 7

Thus;

<P = 7^2 - 11(7) + 146 = 49 - 77 + 146 = 118

<W = 3(7) + 44 = 65

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Answer:

x = 15

Step-by-step explanation:

Given

See attachment

Required

Find x

The figure in the attachment is a quadrilateral and the angles in a quadrilateral add up to 360.

So, we have:

90 + 6x + 5+ 10x - 40 + 4x + 5 = 360

Collect like terms

6x + 10x + 4x = 360 - 90 - 5 + 40 - 5

20x = 300

Divide both sides by 20

x = 15

Hence, the value of x is 15

Answer:

4x+2y=4

3x-y=-7

first one by 3

second by 4

12x+6y=12

12x-4y=-28

subtract

10y=40

y=4

plug in

3x-4=-7

add 4

3x=-3

x=-1

(-1,4)

c

Hope This Helps!!!

Answer: third option

Step-by-step explanation:

There are 2 ways to go about systems of equations normally, and that's elimination and substitution. For this particular problem, I would recommend elimination.

we see the first equation 4x+2y=4

we want to be able to simplify it as much as possible (so it's easier to solve)

so we divide all the terms by 2, giving 2x+y=2.

the second equation can't be simplified, so we set up the elimination method.

   2x+y=2

  -3x-y=-7

multiplying both equations by 2 and 3, we subtract them and get that y equals 4, which is clearly the answer.

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

B.

Step-by-step explanation:

The whole aim here is to get r on it's own. So we have to begin by dividing both sides by pi.

V / pi = hr^2

Then, to further get r on it's own, we have to divide both sides by h. This would put it under the fraction with pi.

V/(pi*h) = r^2

Then, finally, we have to square root both sides.

sqrt(V/(pi*h)) = r

So the answer is B.

Answer:

The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:

3^5 = 243

4^6 = 4096

Since 4096 is greater than 243, we can write:

3^5 < 4^6

or

4^6 > 3^5

Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).

Answer:

y= 0.5 x +2

Step-by-step explanation:

the line crosses the Y line at 2 so you add +2 to the end.   Then you see how far up the line goes every vertical line.

Answer:

y= 0.5 x +2

Step-by-step explanation:

Jarrell should purchase 7 lbs of ground beef.

Number of attendees = 20

Fraction of burger per person = 1/3 lbs

Total fraction of burger required to feed 20 persons :

Number of attendees × fraction per person

20 × 1/3 = 6.667

The number of whole grouhd beef that should be purchased is 7 lbs

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Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

The number of multiple-choice and short-answer questions on a test with 65 questions will be 40 and 25 respectively.

To determine the number of multiple-choice and short-answer questions on a test with 65 questions, we can set up a proportion based on the given ratio:

Multiple-choice questions : Short-answer questions = 8 : 5

Let x be the number of multiple-choice questions.

Let y be the number of short-answer questions.

Using the proportion, we can set up the following equation:

8/5 = x/y

8y = 5x

x = (8y)/5

Since the total number of questions on the test is 65, we have the equation:

x + y = 65

Substituting the expression for x from the previous equation:

(8y)/5 + y = 65

(8y + 5y)/5 = 65

13y/5 = 65

13y = 65 * 5

13y = 325

Dividing both sides by 13:

y = 325/13

y = 25

Substituting this value of y back into the equation x = (8y)/5:

x = (8 x 25)/5

x = 40

Therefore, there are 40 multiple-choice questions and 25 short-answer questions on the test with a total of 65 questions.

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Answer:

A) A car with an initial value of $32,000 is depreciating in value at a rate of 8.5% each year

(B) A job pays a base salary of 12,000 and increases annually at a rate of 7%

Stacy sold 15 children tickets and 30 adult tickets.

The tickets are $7 for adults and $4 for children.

She sells twice as many adult tickets as children tickets and bring in a total of $270.

Therefore,

let

number of children ticket sold = x

number of adult ticket sold = 2x

7(2x) + 4(x) = 270

14x + 4x = 270

18x = 270

x = 270 / 18

x = 15

The number of children ticket sold = 15

The number of adult ticket sold = 15 × 2 = 30

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Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Answer:

y = 9√2

Step-by-step explanation:

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

y² = 9² + x²

By the property of isosceles triangle,

Two angles of the right triangle are equal in measure, opposite sides of these equal angles will be equal in measure.

Therefore, x = 9

y² = 9² + 9²

y² = 81 + 81

y² = 162

y = √162

y = 9√2

The fraction of gas the driver use in one week is 7/10 of a tank.

A fraction is a number which has a numerator and a denominator. such as 7/10

Numerator refers to the upper or top value. 7 is the numerator.

Denominator refers to lower or bottom value. 10 is the denominator.

Fraction of gas the driver use in one week = Fraction of gas used in a day × Number of days in a week

= 1/10 × 7

= (1 × 7) / 10

= 7/10 of a tank

Therefore, the fraction of gas the driver use in one week is 7/10 of a tank.

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Answer:

3

Step-by-step explanation:

12÷3=4

15÷3=5

you can no longer get a lower number without it being a decimal/fraction.

He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.

In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is  tο cοmpare the values, '≤' οr '≥' sign are used.

Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.

300- 80 = 220

220/ 15 = 14.6

Let us say s be the number οf shirts.

Then the inequality will be s≤14

As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.

Hence, the inequality that represents the situatiοn is s≤14.

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Answer:

2.193 cm³

Step-by-step explanation:

density is mass divided by volume:

\(density = \frac{mass}{volume}\)

you can manipulate the formula by multiplying with volume:

\(density \times volume = mass\)

then dividing by density:

\(volume = \frac{mass}{density} \)

in this case:

\(volume = \frac{25g}{11.4 \frac{g}{cm} } = 2.193 { \: cm}^{3} \)

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer: I can't solve all of them but I will give tips. i repeats in cycles so i^1 is sqrt-1, i^2 is -1, i^3 is -i and i^4 is 1. Look at the exponent and first divided out 4 then use the  1 2 3 answers. When you divided i and a number such as (1-i)/1+i) multiply by the conjugate of the denominator which is 1-i. To find conjugate replace the + with a -.

Step-by-step explanation:

Vertical asymptote at x=a if the denominator is zero at x=a and the numerator isn't zero at x=a

Equal the denominator to zero and solve x:

Prove if x=-9/2 makes the numerator equal to 0:

As the value x=-9/2 doesn't make the numerator be equal to zero the function has a vertical asymptote in x=-9/2

_______________

Numerator and denominator have the same largest exponent. Then, the line y=a/b is the horizontal asymptote:

Then, the given function has the next asymptotes:

Vertical asymptote: y= -9/2 (in red)

Horizontal asymptote: x= -4 (in blue)

Hey there!

\(\huge\boxed{\rm{3\%\ of \ 100}}\)

\(\huge\boxed{\rm{= 3\% \times100}}\)

\(\huge\boxed{\rm{= \dfrac{3}{100} \times 100}}\)

\(\huge\boxed{\rm{= 0.03 \times 100}}\)

\(\huge\boxed{\rm{= \dfrac{3\times100}{100\times1}}}}\)

\(\huge\boxed{\rm= \dfrac{300}{100}}}\)

\(\huge\boxed{\rm{\rightarrow\dfrac{300\div100}{100\div100}}}\)

\(\huge\boxed{\rightarrow{\rm{\dfrac{3}{1}}}}\\\\\\\huge\boxed{\rightarrow{3\div1}}\)

\(\huge\boxed{\rm{= 3}}\)

\(\huge\boxed{\mathsf{Answer: 3 }}\huge\checkmark\)

\(\huge\textsf{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

\(\huge\text{Guide: The word \underline{of} means multiply in math}\)

Answer:

The cost of the bottle of drink is P4.85. The refund for an empty bottle is 25 thebe.

To express the refund as a percentage of the cost of the drink, we need to convert the refund to the same unit as the cost of the drink.

1 thebe = 0.038 Philippine pesos (as of June 2023)

25 thebe = 0.95 Philippine pesos

Therefore, the refund for an empty bottle is 0.95/4.85 x 100% = 19.59%

So the refund for an empty bottle is 19.59% of the cost of the bottle of drink.

hope it helps you.....

Mark as brainliest

Answer:

\(A=(17+7\sqrt7)\ m^2\)

Step-by-step explanation:

Given that,

The length of the rectangle, \(l=(3+\sqrt7)\ m\)

The width of the rectangle, \(b=(1+2\sqrt{7} )\ m\)

We need to find the area of the rectangle. We know that the area of the rectangle is given by :

\(A=l\times b\)

Put all the values in the above formula.

\(A=(3+\sqrt7)\times (1+2\sqrt7)\\\\=3+3\times 2\sqrt7 +\sqrt7+2(\sqrt7)^2\\\\=3+6\sqrt7+\sqrt7+14\\\\=(17+7\sqrt7)\ m^2\)

So, the area of the rectangle is \((17+7\sqrt7)\ m^2\).

Answer:

0

Step-by-step explanation:

in the form, y = mx + b, b is the y intercept and m is the slope

y = 9/5 x  can also be written as y = 9/5 x + 0, and 0 is the b value. You can also try to find the y intercept by plugging in 0 for x, which in that case you get:

y = 9/5(0) = 0. again, b is shown to be 0

The volume of the cone is 314cm³

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

The volume of the cone is 1/3πr²h

h²= 13²-5²

h = √169 - 25

h = √144

h = 12 cm

V = 1/3πr²h

V = 1/3 ×3.14 × 5² × 12

V = 942/3

V = 314 cm³

therefore the volume of the cone is 314cm³

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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