Donte is told that for a particular math problem, the value of y is always 8 times the value of x. Donte writes the equation y=8x to show the relationship between x and y. What is the constant of proportionality?

The length of segment DC is given by the law of sines and trigonometric ratios as approximately 11.3 cm

The law of sines states that in a triangle, the ratio of the sine of an interior angle of a triangle to the length of the side opposite the angle is constant.

The given parameters are;

The figure ABC is a triangle

The figure ADC is a straight line segment

Segment BD is perpendicular to segment AC

The length of segment AB = 8 cm

Length of segment BC = 12 cm

The measure

[tex] \angle ABD = 60^{ \circ} [/tex]

Required;

The length of segment DC

Solution;

[tex] \angle ADB = 90^{ \circ} [/tex]

Definition of segment BD being perpendicular to segment AC

[tex] \angle BAC = 90^{ \circ} - 60^{ \circ} = 30^{ \circ}[/tex]

Using the law of sines, we have;

[tex]AD = AB × sin( \angle ABD) [/tex]

A vertex of the triangle from the question is point B

Which gives;

AD = 8 × sin(60°) = 4•√3

Similarly, from the law of sines, we have;

[tex]\displaystyle{\frac{BC}{sin ( \angle BAC)} = \frac{AB}{sin ( \angle BCA)} } [/tex]

Which gives;

[tex] \displaystyle{\frac{12}{sin ( 30^{ \circ})} = \frac{8}{sin ( \angle BCA)} } [/tex]

[tex] \displaystyle{ sin ( \angle BCA) = \frac{sin ( 30^{ \circ}) \times 8}{12}= \frac{1}{3} }[/tex]

[tex] \displaystyle{ \angle BCA = arcsine \left(\frac{1}{3}\right) }[/tex]

[tex] \displaystyle{DC= 12 \times cos\left(arcsine \left(\frac{1}{3}\right)\right) = 8\cdot \sqrt{2}}[/tex]

Therefore, DC = 8•√2 ≈ 11.3

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Answer:

Problem 1.  n=28

Problem 2. a=10

Step-by-step explanation:

I'm not completely sure what you are really trying to accomplish but I think you are trying to do linear equations for these shapes.

Problem 1.

n+4n+40=180

add like terms

5n+40=180

subtract 40 from both sides

5n=140

divide by 5 on both sides

n=28

Problem 2.

7a+10a+12a+7a=360

add like terms

36a=360

divide both sides by 36

a=10

Hope this helps you remember how to do linear equations!

Please give brainliest!

The value of the expression as in the task content is; 1/4.

It follows from the task content that the value of the expression is to be determined.

Hence, since the expression whose value is required to be determined is ; (1 + (1/2))² - 2.

It follows from PEMDAS guidelines that the parentheses be solved first so that we have;

(3/2)² - 2........After solving the parentheses.

Next, the exponent should be solved as follows;

= (9/4) - 2.

And finally, by solving the subtraction; we have;

= 1/4 = 0.25.

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The value of the function at the given value of x = -1 is 5 - 2[f(-1)] = -51

The equation of the function is given as

f(x) = -8x + 20

The function to calculate is given as

5 - 2[f(-1)]

So, we start by calculating the value of the function at x = -1

This is represented as 'f(-1)

So, we have the following equation

f(-1) = -8(-1) + 20

Evaluate the product

So, we have the following equation

f(-1) = 8 + 20

Evaluate the sum

So, we have the following equation

f(-1) = 28

Substitute f(-1) = 28 in the expression 5 - 2[f(-1)]

So, we have

5 - 2[f(-1)] = 5 - 2 x 28

Evaluate the product

5 - 2[f(-1)] = 5 - 56

Evaluate the difference

5 - 2[f(-1)] = -51

Hence, the value is -51

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Therefore, [tex]8\sqrt{2}[/tex] number of inches in the perimeter of new square if the perimeter of the original  square is 16 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

Given: The midpoints of the adjacent sides of a square are connected to form a new square. The perimeter of the original square is 16 inches.

As perimeter is 16 in, so the side is 4 in.

Each side of the new square is the hypotenuse of an isosceles right triangle with legs of length 2 inches.

[tex](2 in)^2 + (2 in)^2 = s^2\\s^2 = 8 in^2\\s = 2\sqrt{2} in[/tex]

Therefore,

Perimeter = 4s

[tex]P = 4(2\sqrt{2}) = 8\sqrt{2} in[/tex]

Therefore, [tex]8\sqrt{2}[/tex] number of inches in the perimeter of new square if the perimeter of the original  square is 16 inches.

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Answer:261

Step-by-step explanation:

4x4x4x4=4x4=16\16x4=64x4=256\256+5=261

We can see that function g(x) is a translation of one unit to the left and 3 units downwards of f(x), thus, the correct options are:

C and E.

Here we have the two functions:

f(x)

g(x) = 4^(x + 1) - 3

And we know that g(x) is a translation of f(x)

Remember that the translations works as follows:

Vertical translation of N units:

g(x) = f(x) + N

If N > 0, the translation is upwards.

If N < 0, the translation is downwards.

Horizontall translation of N units:

g(x) = f(x) + N

If N > 0, the translation is to the left

If N < 0, the translation is to the right.

In this case, we can write g(x) as:

g(x) = f(x + 1) - 3 = 4^(x + 1) - 3

So we will have a translation of one unit to the left and 3 units downwards.

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Answer:

[tex]6x^{2} +17x+12[/tex]

Step-by-step explanation:

(3x+4)(2x+3)

use the FOIL method: that is, multiple first pair, outer pair, inner pair, then last pair:

(3x+4)(2x+3)

(3x × 2x) + (3x × 3) +(4 × 2x) + (4 × 3)

[tex]6x^{2} +9x+8x+12[/tex]

= [tex]6x^{2} +17x+12[/tex]

Answer:

wait nvm it's 23 over 7 as far as I know

Through the unitary method, we get that 8000 tons of petrochemicals are required to produce 5,000 tons of plastic.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value.

Given :

160,000 tons of petrochemicals are required to produce 100,000 tons of plastic.

160,000 tons of petrochemicals produces = 100,000 tons of plastic.

To produce 1 ton of plastic, the required amount of petrochemicals = [tex]\frac{160,000}{100,000} = \frac{8}{5}[/tex] tons...........equation (1)

Let x be the tons of petrochemicals required to produce 5,000 tons of plastic.

Multiplying 5,000 tons on both sides of the equation, we get :

To produce 5,000 tons of plastic =[tex]\frac{8}{5}*5000 = 8000[/tex] tons of petrochemicals

Hence, 8000 tons of petrochemicals are required to produce 5,000 tons of plastic.

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The graph shows the proportional relationship between the amount of time (in minutes). Points (6,3) represent the time required to plant 3 petunias will be 6 minutes.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that there is a proportional relationship between the amount of time (in minutes) Jennifer has been working in her garden, x, and the number of petunias she has planted, y

Points 6 represent the time required to plant 3 petunias i.e. 6 minutes.

Points 3 represent the number of petunias i.e 3.

This indicates that after spending 6 minutes in his garden, he plants 3 petunias.

Thus, the graph shows the proportional relationship between the amount of time (in minutes). Points (6,3) represent the time required to plant 3 petunias will be 6 minutes.

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Answer:

58.

Step-by-step explanation:

The number of students who travelled by bus = 473 - 9 = 464.

So, the number of students in each bus = 464/8

= 58.

[tex]70x = 4 - 5 \\ 70x = - 1 \\ \frac{7 0x}{70} = \frac{ - 1}{70} \\ x = - \frac{1}{70} [/tex]

HOPE THIS HELPS.

Answer:

[tex]-1 \le x\le1.5[/tex]

Step-by-step explanation:

The expression we're given, we want both to be defined because how can you add a defined number to an undefined number?

Square roots only have real solutions for positive numbers and zero

So let's set up an inequality for both square roots

[tex]2x+2\ge0\\\\6-4x\ge0[/tex]

Let's solve the first one

[tex]2x+2\ge 0\\2x\ge-2\\x\ge-1[/tex]

this is the domain of the "first expression"

let's solve the second one

[tex]6-4x\ge 0\\-4x\ge -6\\x\le 1.5[/tex]

We want them to overlap, so we get a compound inequality: [tex]-1 \le x\le1.5[/tex]

since we want both of the expressions to be defined to define the entire thing.

The value of the quotient of the polynomials is 2x - 1

The polynomials are given as

2x² + x - 15

x + 3

Where

Dividend = 2x² + x - 15

Divisor = x + 3

The quotient of the polynomials is calculated as

Quotient = Dividend/Divisor

Substitute the known values in the above equation

So, we have

Quotient = (2x² + x - 15)/(x + 3)

Factorize the numerator

Quotient = (x + 3)(2x - 1)/(x + 3)

Cancel out the common factors

Quotient = 2x - 1

Hence, the quotient is 2x - 1

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Answer:

Physical means the actual wires.  Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.

a. Logical

Step-by-step explanation:

...

The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).

The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.

A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.

Therefore, the arrangement of network cabling between devices is a physical topology.

Hence, the correct answer would be an option (C).

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Total of 10 and $ total of $0.85. The place value denotes a word, whereas the total value denotes a figure. In mathematics, ten numbers are known as symbols or digits.

The sum of the digit and its place value is the total value. Example 1: In the number 58439, what is the place value of digit 4? As a result, digit 4's place value is Hundreds. Market capitalization is the value of a company as determined by the stock market. It is defined as the sum of all outstanding shares' market values. Multiply the number of outstanding shares by the current market value of one share to calculate a company's market cap.

Therefore,

a # total of 10

a $ total of $0.85

·        Since we have 2 unknowns, we need to set up a System of 2 Equations.

·        A System of 2 Equations helps us solve a situation with 2 Unknowns.

Let's set up our 2 equations for # and $.

·        For the # equation:

Let n = # of nickels

Let d = # of dimes

So, n + d = 10

·        For the $ equation, we have to assign a "value" to each of the coins:

A nickel is worth 5 cents or $0.05

A dime is worth 10 cents or $0.10

·        They told us we have 5 cents, a specific # of times + 10 cents, a certain # of times, that = $0.85

So,   $0.05n + $0.10d  

        = $0.85

To solve this, we have to have just 1 unknown, meaning just 1 variable.

· We represent one of the variables in terms of the other. But, which one?

·        Well, since they are asking for # of dimes, let's define a nickel in the duration of a dime.

·        Let's apply this in the simpler # equation:

So, n + d = 10

becomes n = 10 - d

·        So now, in our $ equation, we can just replace "n" with "10 - d", and then solve for d, which is the # of dimes!

$0.05n + $0.10d = $0.85

$0.05(10-d) + $0.10d = $0.85

$0.5 - $0.05d + $0.10d = $0.85

$0.50 + $0.05d = $0.85

$0.05d = $0.35

d = 7

Check this with the # equation:

n + d = 10

n + 7 = 10

n = 3

Does that make sense? Let's see:

3 nickels + 7 dimes = $0.85 ?

3($0.05) + 7($0.10) = $0.85

$0.15 + $0.70 = $0.85

$0.85 = $0.85

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Answer: 5.36 gallons

Step-by-step explanation:

0.64 gallons [liquid] are equal to 0.16907 litre

6 - 0.64 = 5.36

Answer is

-4 < -1 < -1% < 1 < 6

x + y - 6  is equation of slope-intercept form for the perpendicular bisector of the line segment .

What is slope-intercept form explain?

We use formula

                        [tex]\frac{y - y_{1} }{y_{2} - y_{1} } = \frac{x - x_{1} }{x_{2} - x_{1} }[/tex]

                 [tex]\frac{y - 7 }{- 3 - 7} = \frac{x - (-1)}{9 - (-1)}[/tex]

                  y - 7/-10 = x+ 1/10

               10(y-7) = -10( x + 1 )

              10y - 70 = -10x - 10

             10x + 10y - 70 + 10 = 0

            10x + 10y - 60 = 0

           10( x + y - 6 ) = 0

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Answer:

D

Step-by-step explanation:

y=mx+b

-5x is the slope, because it has an x with it

4 is the y-intercept cause it is alone. making it be b also know as the y-intercept

Given:

The function is,

a) The graph of the given function us,

Answer: option B)

b) f(1) and f(5) is,

Answer:

c) the domain of the function is,

The total cost of the bat, the glove, and the baseballs is $88.5 and this can be determined by using the given data and arithmetic operations.Given :He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75.The following steps can be used to evaluate the total cost:Step 1 - Find the cost of the bat after the discount.= $34.5Step 2 - Find the cost of the glove after the discount.= $37.5Step 3 - Now, evaluate the cost of the baseballs.= $16.5Step 4 - Add all the costs to determine the total cost.= 16.5 + 37.5 + 34.5 = $88.5

Answer:

The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.

Step-by-step explanation:

Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.

Each box of chocolate chip cookies has 36 cookies.

Each box of sugar cookies has 84 cookies.

So, the total number of chocolate chips cookies will be = 12 * 36 ----(i)

And the total number of sugar cookies will be = 24 * 84 -----(ii)

As Mia says she has about 1,800 cookies in all.

So, we can write (i) and (ii) combined as,

(12*36) + (24*84) = 1800

The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.

Explanation: No, her answer is not reasonable.

Step by Step solution:

According to the given information, Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.

Now, each box of chocolate chip cookies has 36 cookies which means she has (36 × 12) = 432 chocolate chip cookies in total, using the unitary method.

Also, each box of sugar cookies has 84 cookies which means she has (84 × 24) = 1008 sugar cookies in total, using the unitary method.

Mia will then have with her in total of [(36 × 12) + (84 × 24)] = 1440 cookies.

It is an incorrect fact that Mia says that she has about 1800 cookies in total.

Hence, Mia has 1440 cookies in total.

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Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

79.

Domain: (all real numbers)

Range: [1 to infinity)

x-int: none

y int: (0,1)

Function Value: 2 and 4

80.

Domain: (0 to infinity)

Range: [-1 to infinity)

x-int: none

y int: (0,1)

Function Value: 1

Answer: a meter of timber is 5$

Answer:

Rs5

Step-by-step explanation:

40m =Rs 200

Therefore, 1m = 200/40

= Rs 5