Given that OA =3x+7y
OB = 5x+6y and CD =6x-3y
Explain the geometrical relationship between the straight lines AB and CD.
(I know its parallel but how to prove?)

The expression "eight more than the sum of a number and 7 is 90" can be written as: 8 + (x + 7) = 90

From the question, we have the following parameters that can be used in our computation:

eight more than the sum of a number and 7 is 90

Express the numbers properly

So, we have

8 more than the sum of a number and 7 is 90

Express the operators properly

8 + (x + 7) = 90

hence, the expression is 8 + (x + 7) = 90

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Answer: 7 batches

Step-by-step explanation:

If Eduardo makes 4 batches, he will need 2/3 x 4 = 8/3 cups of flour.

To add 3 more batches, he will need 3 x 8/3 = 8 cups of flour.

In total, Eduardo will need 8/3 + 8 = 32/3 + 8 = 32/3 + 24/3 = 56/3 cups of flour for 7 batches. Therefore, Eduardo will need 8 cups of flour if he makes 3 more batches, and he will need 56/3 cups of flour in total if he makes 7 batches.

Answer: the length is 6

Step-by-step explanation:

3+3+6+6=18

3x6=18

The solution to equation 1, 2, 3, 4, 5 and 6 are y = (-3/2) + 6, y = (-5/3) + 3,  y = (-1/5)x + 9/5, y = (1/4)x + 3/2, y = (-7/3)x + 3 and y = 6x + 3 respectively.

Given the linear equations in the question;

To make y the subject of the formula, we need to isolate y on one side of the equation by moving all other terms to the other side.

1) 3x + 2y = 12

Subtract 3x from both sides:

3x - 3x + 2y = -3x + 12

2y = -3x + 12

Divide each term by 2

2y/2 = -3x/2 + 12/2

y = (-3/2) + 6

2) 5x + 3y = 9

Subtract 5x from both sides:

5x - 5x + 3y = -5x + 9

3y = -5x + 9

Divide each term by 3

3y/3 = -5x/3 + 9/3

y = (-5/3) + 3

3) x + 5y = 9

Subtract x from both sides:

x - x + 5y = -x + 9

5y = -x + 9

y = (-1/5)x + 9/5

4) -2x + 8y = 12

8y = 2x + 12

y = (2/8)x + 12/8

y = (1/4)x + 3/2

5) -7x - 3y = -9

-3y = 7x - 9

y = (-7/3)x + 3

6) 6x - y = -3

-y = -6x - 3

y = 6x + 3

Therefore, the formula in terms of x is: y = 6x + 3.

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To find the area of the given circle we have to use the formula πr², where π=22/7 and r is radius of the circle. The area of the circle is 1519.76 square feet.

A circle is a closed two-dimensional figure in which all sets of points in the plane are equidistant from a specific point called the "center". A line passing through the circle forms a line of specular symmetry. It is also rotationally symmetrical about the center at any angle. 

Solution for the area of the circle:

Given, radius = 22 feet

∴Area of the circle = πr²

                               = (22/7)×22²

                               = 3.14 × 484

                               = 1519.76 square feet

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So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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Harry has  90 mosquitoes on his uniform after the loop de loop.

An integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations

To find the number of mosquitoes that splat on Harry's uniform during the loop de loop, we need to integrate the mosquito density function M(x,y,z) over the curve given by the parametrization r(t):

[tex]\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _{t_1}^{t_2}\:M\left(r\left(t\right)\right)\:||r'\left(t\right)||\:dt\:[/tex]

where C is the curve defined by r(t), ||r'(t)|| is the magnitude of the tangent vector to the curve, and ds is the arc length element.

We can compute the tangent vector to the curve as:

[tex]r'\left(t\right)\:=\: < 7,\:3cos\left(t\right),\:-3sin\left(t\right) >[/tex]

The magnitude of the tangent vector is:

[tex]||r'\left(t\right)||\:=\:\sqrt{7^2\:+\:3^2cos^2\left(t\right)\:+\:3^2sin^2\left(t\right)}\:=\:\sqrt{67}[/tex]

Substituting these expressions into the integral, we get:

[tex]\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _0^{5\pi }\:\frac{12+3cos\left(t\right)}{\pi \sqrt{58}}\sqrt{67}\:dt\:[/tex]

[tex]\int _C\:M\left(x,y,z\right)\:ds\:\approx \:89.62[/tex]

Hence, Harry has  90 mosquitoes on his uniform after the loop de loop.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &708000\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A = 708000(1 - 0.16)^{10} \implies A=708000(0.84)^{10}\implies A \approx 123830.07[/tex]

Given:-

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Solution:-

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Hope it helps! :)

As the total of Rita and Shova's current ages is 20, they are both 20 years old.

A mathematical strategy for resolving proportional and ratio issues is called the unitary method. Finding the value of one unit of an amount and using that value to calculate the value of additional units is what this process entails. The foundation of the unitary approach is the idea that if two quantities are equal, then their ratios must also be equal. For instance, if five apples cost $10, then the expense-to-apple ratio is 10/5 = 2. This ratio can be used to calculate the price of a varied quantity of apples.

given

According to the issue statement, Rita was three times as old as Shova when her age and Shova's current age were equal.

R - (S - R) Equals 3(S - R) (S - R)

When we simplify this solution, we obtain:

2R = 4S - 2S

2R = 2S

R = S

As a result, we are aware that Rita and Shova are both currently the same age.

Additionally, we are aware that their combined current ages are 40 years.

R + S = 40

R = S, so we can change S in the second equation to R:

R + R = 40

2R = 40

R = 20

Rita is currently twenty years old. Since R = S, Shova is 20 years old at the moment.

As the total of Rita and Shova's current ages is 20, they are both 20 years old.

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The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )

Answer:

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

25% of 84 is 21

Step-by-step explanation:

25% can be written as 0.25

0.25 times 84 = 21

As the x-value increases, the function decreases towards y = 0. Then the correct option is C.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as,

y = a(b)ˣ

The exponential function is given below.

f(x) = (0.4)ˣ

As x tends to positive infinity, then the value of the function is calculated as,

[tex]\rm f(x) = (0.4)^{\infty}\\\\f(x) = 0[/tex]

As the x-value increases, the function decreases towards y = 0. Then the correct option is C.

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Answer: 9 and 3

Step-by-step explanation: Depends the signs +/- and the problem.

Answer:

8.407

Step-by-step explanation:

8.767−0.36

= 8.767−0.36

=8.767+(−0.36)

= 8.407

Answer:

B I did the math in my head mb if I get wrong

Let's start by using "x" to represent the number of picture cards that Cevin has. We know that Tom has 3 times as many picture cards as Cevin, so:

Tom = 3x

We also know that Tom has 2304 picture cards, so:

3x = 2304

Solving for x, we get:

x = 768

So, Cevin has 768 picture cards.

We also know that Ron has 190 fewer picture cards than Kevin, so:

Ron = x - 190

Substituting x with 768, we get:

Ron = 768 - 190

Therefore, Ron has:

Ron = 578 picture cards.

Answer:1.111

Step-by-step explanation:

Let's use the variable W to represent the percent of top earners who are women.

According to the problem statement, the percent of top earners who are men is more than four and a half times the percent of top earners who are women. Mathematically, we can write this as:

M > 4.5W

Additionally, the percent of top earners who are men is less than five times the percent of top earners who are women. This can be written as:

M < 5W

We can combine these two inequalities into a compound inequality:

4.5W < M < 5W

This means that the percent of top earners who are men is between 4.5 times and 5 times the percent of top earners who are women.

To solve for W, we can divide all three parts of the compound inequality by 4.5:

W < M/4.5 < W/0.9

Simplifying, we get:

W < 0.222M < 1.111W

Therefore, the percent of top earners who are women, W, must be less than 0.222 times the percent of top earners who are men, and also less than 1.111 times the percent of top earners who are women.

series: 12, 11, 13, 12, 14, 13, … What number should come next? i believe its 12

12-11=1

13-11=2

So to get 11 you subtract 1 from 12 and to get 13 you add 2 to it

If you follow that procedure the next number should be 15 if you add 2 to 13

A good book is one that makes the reader feel. It takes the reader on a compelling journey. .

A book is a medium for recording information in the form of writing or images, typically composed of many pages bound together and protected by a cover

Given is to understand what are the characteristics of good book.

A good book is one that makes the reader feel. It takes the reader on a compelling journey.

Calling a book “good” is an opinion that can be applied to any book.

Therefore, a good book is one that makes the reader feel. It takes the reader on a compelling journey.

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An equation for the relation is y = -3x + 10.6.

f(50) is -139.4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (1, 7.6), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 7.6 = (4.6 - 7.6)/(2 - 1)(x - 1)

y - 7.6 = -3(x - 1)

y = -3x + 3 + 7.6

y = -3x + 10.6

For f(50), we have:

y = -3x + 10.6

y = -3(50) + 10.6

y = -150 + 10.6

y = -139.4

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Answer:

a and b

Step-by-step ex

Answer:

Step-by-step explanation:

A.  h = -2(1)² + 7(1) + 4 = 9 ft

B.  use the quadratic formula to find the 2 solutions to t when

y = f(t) = -2t² + 7t + 4 = 0         a=-2, b=7, c=4

the 2 solutions for t are:  -1/2, 4

halfway between t=-1/2 and t=4 is:  (-1/2 + 4) /2 = 1.75   (vertex of the parabola)

so, at t = 1.75 s, the toy is at its max. height:

h = -2(1.75)² + 7(1.75) + 4 = 10.125 ft

C.  Toy is in the air for 4 sec

The answer is 4 s because f(4) = 0, meaning the toy hits the ground after 4 sec

Answer:

C) 36.

Step-by-step explanation:

Since there are 9 game pieces in each tic-tac-toe board and the class has 4 tic-tac-toe boards, the total number of game pieces the class has is:

9 pieces/board x 4 boards = 36 pieces

Therefore, the answer is C) 36.

Answer:

Step-by-step explanation:

a. 4x + 8

b. 14x

c. 8x + 12

d. 6x + 6y + 6z

Answer:

Step-by-step explanation:

1]4(x+2)

using distributive property ,

Multiply 4 to x and 2

4x + 8

2]4(2x+3)

using distributive property ,

Multiply 4 to 2x and 3

= 4 x 2x + 4 x 3

= 8x +12

3](6 + 8).x

= (14).x

14x

4] 6(x + y + z)

using distributive property ,

multiply 6 to x and y and z

6.x + 6.y + 6.z

6x + 6y +6z

Answer:

it 39 ×90 for sure it 3510

Therefore , the solution of the given problem of area  comes out to be potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).

Its total size can be determined by how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. The sum of the boundaries for each of a cuboid's six rectangular edges represents its internal water capacity. To calculate the size of the box, use the following method:

Here,

Let's write L for the rectangular plot's length and W for its breadth. Consequently, the rectangle plot's perimeter can be written as:

=> 2L + W = 53

Additionally, since we are aware that the rectangle plot's area is 306, we can write:

=> LW = 306

By resolving the initial solution for W, we can obtain:

=> W = 53 - 2L

When we use this formula as W's substitute in the second equation, we obtain:

=> L(53 - 2L) = 306

Increasing the left edge gives us:

=> 53L - 2L² = 306

Rearranging and condensing results in:

=> 2L² - 53L + 306 = 0

To find L, we can use the cubic formula:

=> L = [53 + √53² - 4(2)(306))] / (2(2))

=> L = [53 ± 25] / 4

=> L = 19 or L = 8

The rectangular plot's two groups of potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).

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Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

Given

[tex]\left(4^4\right)^{-1}[/tex]

We can use the power rule to multiply the exponents.

The power rule for exponents states

[tex]\left(a^b\right)^{c}=a^{bc}[/tex]

[tex]4^{4*-1}[/tex]

Multiply 4 by −1.

[tex]4^{-4}[/tex]

Rewrite the expression using the negative exponent rule.

The negative exponent rule states

[tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]\frac{1}{4^4}[/tex]

Raise 4 to the power of 4.

[tex]\frac{1}{256}[/tex]

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The side AC is 10 units long.

Measurement of length can be done in a variety of methods, including using handspan, foot span, metres, or other units including millimetres, inches, and metres. There are two types of length measurement units: There are both conventional and nonstandard length measurement units.

The Pythagorean theorem can be used to determine the length of side AC in the triangle ABC given:

AC² = AB² + BC²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

AC = 10

As a result, the side AC is 10 units long.

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