Find the equation of a line parallel to x-axis at a distance of 2 units below x-axis.

The value of the sin A in simplest radical form is 0.651 units

From the Figure,

We have the following information :

The triangle in the image is Right angle triangle.

The value of side AB is [tex]\sqrt{85}[/tex].

The value of side BC is 6.

The value of side CA is 7.

And we know that :

In the Right angle triangle, One angle is 90 degree.

So, The value of angle ABC is 90 degree.

For solving, we use the sin law:

Sine law-The law of sine can be used to calculate the remaining sides or angle of the triangle when 2 or more sides or angle are known.

[tex]\frac{AB}{SinC} =\frac{BC}{Si nA }[/tex]

Plug all the values in above formula:

[tex]\frac{\sqrt{85} }{Sin 90} =\frac{6}{Sin A}[/tex]

Now, Solving value of Sin A

Sin A = (6 × sin 90)/[tex]\sqrt{85}[/tex]

Sin A = 6 /[tex]\sqrt{85}[/tex]

Sin A = 0.651

Hence, the value of the sin A in simplest radical form is 0.651 units.

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The additional number of pennies needed to complete 1 dime is 3

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

Pennies = 7

As a general rule

Ten pennies have the same value as 1 dime.

This means that

7 pennies + x = 1 dimes

So, we have

7 pennies + x = 10 pennies

Where x is the additional pennies needed

When evaluated. we have

x = 3

Hence, the additional number of pennies needed is 3

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The solution of the sine function sin(5π/12) is (√6 + √2)/4.

As per the sum and difference identity for sine, which states:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

To find sin(5π/12), we can express it as the sum or difference of two angles whose sine values we know.

One possible way is to use the fact that:

5π/12 = π/4 + π/6

So we have:

sin(5π/12) = sin(π/4 + π/6)

Using the sum identity, we get:

sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)

We know that sin(π/4) = cos(π/4) = √2/2 and sin(π/6) = 1/2, so we can substitute:

sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)

simplify the expression:

sin(π/4 + π/6) = (√6 + √2)/4.

Therefore, sin(5π/12) = sin(π/4 + π/6) = (√6 + √2)/4.

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The solution is :

The length of the rectangle is L=18cm

The width of the rectangle is W=10cm

We have,

Given data

let the length be x

L=x

Width= x-8

W= x-8

Perimeter= 56cm

But we know that the perimeter is expressed as

P=2L+2W

substitute our data

56=2(x)+2(x-8)

56=2x+2x-16

56+16=4x

72=4x

divide both sides by 4

x= 72/4

x=18cm

Hence the Length is 18cm

L=18cm

The width= 18-8

W=10cm

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complete question:

Arectangle has a width that is 8 centimeters less than its length. The perimeter of the rectangle is 56 centimeters. Find both the width and length of the rectangle. Show your work.

In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

Since, We know that;

In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

This balance is important because too much excitatory signaling can cause overstimulation and potential harm, while too much inhibitory signaling can lead to neural suppression and lack of responsiveness.

Hence, The proper balance between the two types of signals is necessary for healthy neuronal activity, and maintaining that balance is a key aspect of neural health.

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The circular is around 305 cm in circumeference.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting d = 97 cm and using the value of π to be 3.14159, we get:

C = πd

C = 3.14159 × 97 cm

C ≈ 304.731 cm

Rounding this to 3 significant figures, we get:

C ≈ 305 cm

Therefore, the circumference of the circle is approximately 305 cm.

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After 6 years, the investment is whort $4,051.97

We know that this can modeled by an exponential equation of the form:

y = A*(1 + r)^x

Where A is the initial amount and r is the rate at which the investement grows (in decimal form)

Then we can write the equation as:

y = 2700*(1 + 0.07)^x

Where x is the number of years.

Then after 6 years, the investment is whort:

y = 2700*(1 + 0.07)^6 = 4,051.97

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The first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the first circle:

28° = x - 61° {secant tangent angle}

x = 28° + 61°

x = 89°

y² = 4 × 18

y = √72

y = 8.4853

For the second circle:

triangles formed by intersecting tangents are congruent so;

x = 2 × [180 - (24 + 90)]

x = 2 × 66°

x = 132°

tan 24 = 7/y {opposite/adjacent}

y = 7/tan 24

y = 15. 7223

For the third circle:

9(9 + a) = 21 × 8 {secant secant}

81 + 9a = 168

9a = 168 - 81

9a = 87

a = 87/9

a = 9.6667.

Therefore, the first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

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The account balance after 7 years = $1,547.48

We know that the formula for the compound interest is:

[tex]A = P(1 + r/n)^{nt}[/tex]

where,

A = amount (principal + interest)

P = Principal amount

R = interest rate as a percent

r = interest rate as a decimal

n = number of compounding periods

and t = time in years

Here, P = $700, t = 7 and R = 12%

First, convert R as a percent to r as a decimal

r = R/100

r = 12/100

r = 0.12 rate per year,

Using above formula, the amount after 7 years would be,

[tex]A = P(1 + r/n)^{nt}[/tex]

[tex]A = 700.00(1 + \frac{0.12}{1} )^{1\times 7}[/tex]

A = 700.00 × (1 + 0.12)⁷

A = $1,547.48

Therefore, the total amount accrued on a principal of $700.00 at a rate of 12% per year compounded 1 times per year over 7 years is $1,547.48.

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Answer:

In this situation, [tex]t[/tex] (time) is the independent variable, and [tex]p[/tex] is the dependent variable, since calculating it relies on [tex]t[/tex]. In a real-world context, [tex]p[/tex] represents the number of hard drives sold in [tex]t[/tex] number of years.

Answer:

62500

Step-by-step explanation:

To multiply 250 and 25, we can first multiply the two numbers ignoring their zeroes and then add the zeroes back in the product.

250 multiplied by 25 is:

25 × 25 = 625 (ignoring the zeroes)

250 × 25 = 62500 (adding the zeroes back in)

Therefore, 250 multiplied by 25 is equal to 62500.

The vertex of the parabola is at approximately (15, 2,350) which means that the maximum daily profit occurs when the price of each solar panel is increased by $5 fifteen times.

The function P(x) = −6x² + 180x + 1,000 models the daily profit of a company

where;

x = number of $5 price increases for each solar panel.

The vertex form of the quadratic function is P(x) = a(x-h)² + k

where;

(h,k) = vertex of the parabola.

To find the vertex, we can use the formula h = -b/2a and substitute the values of a, b, and c from the given function.

In this case, a = -6, b = 180, and c = 1000.

h = -b ÷ 2a

h = -180 ÷ (2 × (-6))

h = 15

So the x-coordinate of the vertex is 15.

To find the y-coordinate, we can substitute x=15 into the original function:

P(15) = -6(15)² + 180(15) + 1,000

P(15) = 2,350

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The equation of the line in slope-intercept form is; y = 6x - 5

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope (m) represents the rate of change of the line, which is the amount by which y changes when x increases by 1. The y-intercept (b) represents the point at which the line intersects the y-axis.

By using the slope-intercept form of a line, we can easily graph a line by plotting the y-intercept and then using the slope to find additional points on the line.

For the given line, the slope is 6 and the y-intercept is -5.

Therefore, the equation of line in slope-intercept form is;

y = 6x - 5

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The total 'x' number of cups of trail mix  Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

Orly uses 3 cups of raisins for every 10 cups of trail mix,

Which means that the ratio of cups of raisins to cups of trail mix is 3:10.

let us consider x be the number of cups of trail mix

and c be the number of cups of raisins.

We can set up a proportion to solve for the number of cups of trail mix,

⇒ 3/10 = c/x

To solve for x, we can cross-multiply and simplify,

⇒ 3x = 10c

⇒ x = 10c / 3

Therefore, if Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

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Answer:

8%: $295

10% : $6005

15%: $595

Step-by-step explanation:

Let's break this down:

Let's call the amounts invested at 8% and 10% combined = x
Then call the amount invested at 15% = x + $300
8% of x = 0.08x
10% of (6300 - x) = 0.1(6300 - x)
15% of (x + $300) = 0.15(x + $300)
0.08x + 0.1(6300 - x) + 0.15(x + $300) = $773
0.18x = $53
x = $53/0.18 = $295

a = amount invested at 8%

how much is 8% of "a"? (8/100) * "a", namely 0.08a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 15%

how much is 15% of "c"? (15/100) * "c", namely 0.15c.

we know the total amount invested is 6300, so whatever "a", "b" and "c" might be, we know that a + b + c = 6300.

we also know that the yielded amount in interest is 773, so if we simply add their interest, that'd be 0.08a + 0.10b + 0.15c = 773.

we also know that the combined amounts of "a + b" plus 300 bucks is "c", so really c = a + b + 300.

[tex]c = a + b + 300 \\\\[-0.35em] ~\dotfill\\\\ a+b+c=6300\implies c=6300-a-b\implies \stackrel{\textit{substituting from the equation above}}{a+b+300=6300-a-b} \\\\\\ 2a+2b+300=6300\implies 2a+2b=6000\implies 2(a+b)=6000[/tex]

[tex]a+b=\cfrac{6000}{2}\implies a+b=3000\implies \boxed{b=3000-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c = a + b + 300}\implies \stackrel{\textit{substituting from above}}{c=a+(3000-a)+300}\implies {\Large \begin{array}{llll} c=3300 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{we also know that} }{0.08a+0.10b+0.15c=773}\implies \stackrel{\textit{now, substituting "b" and "c"}}{0.08a+0.10(3000-a)+0.15(3300)=773}[/tex]

[tex]0.08a+300-0.10a+495=773\implies -0.02a+300+495=773 \\\\\\ -0.02a+795=773\implies -0.02a=-22\implies a=\cfrac{-22}{-0.02}\implies {\Large \begin{array}{llll} a=1100 \end{array}} \\\\\\ \stackrel{\textit{now, we know that}}{b=3000-a}\implies {\Large \begin{array}{llll} b=1900 \end{array}}[/tex]

The answer of the given question based on the equation is , the unknown number is 6.

An equation is the  mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.

The statement can be translated into an equation as follows:

2(y - 2) = 8

Simplifying the equation, we can distribute the 2 on the left-hand side:

2y - 4 = 8

Then, we can add 4 to both sides to isolate the variable:

2y = 12

Finally, we divide both sides by 2 to solve for y:

y = 6

Therefore, the unknown number is 6.

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Answer:

63.67

Step-by-step explanation:

nice one, this got me thinking some time

The total number of books in all the piles is 4 x  72 = 288.

For one to be able to create the equal stacks of books in all  of the four styles, one need to look at the greatest common divisor (GCD) .

Hence the GCD of 300, 90, 6, and 180:

300 = 2² x  3  x  5²

90 = 2 x  3²  x  5

6 = 2 x  3

180 = 2²  * 3²  *x 5

The GCD is 2²  x 3²  = 36.

In terms of the number of piles, we have to divide the total number of books in all of the style by the GCD: Hence:

300 ÷  36 = 8.33...

90  ÷ 36 = 2.5

6  ÷ 36 = 0.17...

180 / ÷ 36 = 5

For one to be able to find the total number of books in all of pile, we need to multiply the GCD by the number of piles:

36 x  2 = 72

Hence, each pile will need to contain 72 books. The total number of books in all the piles is 4 x  72 = 288.

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Answer:

72 such cuboids are required to make a perfect cube.

Step-by-step explanation:

V = l x w x h

V = 12 cm x 9 cm x 8 cm = 864 cm^3

edge length = V^(1/3) = (864 cm^3)^(1/3) = 12 cm

V_cube = edge length^3 = 12 cm^3

number of cubes = V_cuboid / V_cube = 864 cm^3 / 12 cm^3 = 72

Therefore, 72 such cuboids are required to make a perfect cube.

The equation is solved and the distribution property is given by

a) A = 5x + 15

b) B = x² - 3x

c) C = x² + 6x + 8

d) D = x² - 10x + 25

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = 5 ( x + 3 )

On simplifying the equation , we get

A = 5 ( x ) + 5 ( 3 )

A = 5x + 15

b)

B = x ( x - 3 )

On simplifying the equation , we get

B = x ( x ) - x ( 3 )

B = x² - 3x

c)

C = ( x + 4 ) ( x + 2 )

On simplifying the equation , we get

C = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 )

C = x² + 4x + 2x + 8

C = x² + 6x + 8

d)

D = ( x - 5 ) ( x - 5 )

On simplifying the equation , we get

D = ( x - 5 ) ( x ) + ( x - 5 ) ( -5 )

D = x² - 5x - 5x + 25

D = x² - 10x + 25

Hence , the equations are solved

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Answer:

25480

Step-by-step explanation:

Hopefully it's right.

The approximate number of people who will receive a small prize at this year's fair is 12,000.

What is number?

A number is a mathematical concept used to represent a quantity or value. It can be represented by numerals, symbols, or words.

To estimate the number of people who will attend this year's fair, we can calculate the average attendance of the last 5 years:

Average attendance = (270,000 + 280,000 + 300,000 + 320,000 + 330,000) / 5

= 300,000

Therefore, a reasonable estimate of the number of people who will attend this year's fair is 300,000.

To find the approximate number of people who will receive a small prize at this year's fair, we need to multiply the number of people who receive raffle tickets by the proportion of those who will receive a small prize:

Number of people who will receive a small prize = 60,000 x 0.2

= 12,000

Therefore, the approximate number of people who will receive a small prize at this year's fair is 12,000.

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Answer:

This question is not fully filled out.

Answer:

This is the formula:

1 degree = π/180 radians

To convert 70 degrees to radians, we can multiply by the conversion factor:

70 degrees × π/180 = 7π/18 radians

So 70 degrees is equal to 7π/18 radians.:)

Answer:  B, D, A

Step-by-step explanation:

1. In order to be greater than 0 when multiplying 2 numbers they must be the same sign so that happens in quadrant 1 an 3.   B

2. y is negative in quadrant 3 and 4 which are below the x-axis.  D

3.  since x=0 is a line that goes up and down.  It' along the y-axis. A

Answer:

(d)  Option 2 - The set of all points in quadrants I and III {x and y have the same sign}.

(e)  Option 4 - The set of all points below the x-axis.

(f)  Option 1 - The set of all points on the y-axis.

Step-by-step explanation:

xy > 0 means that the product of x and y is positive.

This is true if both x and y have the same sign (either both positive or both negative).

In quadrant I all points have both a positive x and y coordinate.

In quadrant III all points have both a negative x and y coordinate.

Therefore, the correct answer is:

[tex]\hrulefill[/tex]

y < 0 means that y is negative.

All points above the x-axis have a positive y-coordinate.

All points below the x-axis have a negative y-coordinate.

The y-coordinate of all points on the x-axis is equal to zero.

Therefore, the correct answer is:

[tex]\hrulefill[/tex]

x = 0 means that x is equal to zero.

All points on the x-axis have:

All points on the y-axis have:

The coordinates of the origin are (0, 0).

Therefore, the correct answer is:

The graph of [tex]g(x) = 10^{(x+2)} +3[/tex] will be the graph of [tex]f(x) = 10^x[/tex] shifted left by 2 units and up by 3 units. It will still be an increasing exponential function that passes through the point (-2,4) instead of (0,1).

What is graph?

In mathematics, a graph is a visual representation of the relationships between objects. A graph consists of vertices, which are points or nodes, and edges, which are lines or arcs connecting the vertices.

To understand the transformation of the graph of [tex]g(x) = 10^{(x+2)} +3[/tex], we can first examine the basic graph of [tex]f(x) = 10^x[/tex]. This graph is an increasing exponential function that passes through the point (0,1), and as x gets larger, the y-values grow at an increasingly rapid pace.

Now let's consider the transformations applied to f(x) to obtain g(x):

The "+2" inside the exponent of [tex]10^{(x+2)[/tex] shifts the graph of f(x) to the left by 2 units. This means that the point (0,1) on the graph of f(x) will be moved to the left to the point (-2,1) on the graph of g(x).

The "+3" added outside the exponent of [tex]10^{(x+2)[/tex] shifts the entire graph of f(x) upwards by 3 units. This means that every point on the graph of f(x) will be shifted up by 3 units to obtain the corresponding point on the graph of g(x).

Therefore, the graph of [tex]g(x) = 10^{(x+2)} +3[/tex] will be the graph of [tex]f(x) = 10^x[/tex] shifted left by 2 units and up by 3 units. It will still be an increasing exponential function that passes through the point (-2,4) instead of (0,1).

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-32t + 220

= -32(12) + 220

-384 + 220 =

-164

first step is to take the derivative. next is to plug in 12 into the function

Answer: g(x)= -|x|

.

Step-by-step explanation:

a|x-h|+k  

> this form shows the shifts, stretches and reflections

> If there is a h or k, the vertex has shifted to (h, k)

> "a" is your stretch

> if there is a - in front, the function has been refected

The image you gave is facing upside down so it's been reflected.  There has been no other changes the (h, k) is (0,0) and there has been no stretch

g(x)= -|x|       just put a negative in front to show reflection.

A and B are mutually exclusive events, so PA) is 11/20.

Given that, P(B)=1/5 and P(A or B)=3/4.

For mutually exclusive events A and B

That is, P(A or B) = P(A) + P(B)

Here, 3/4 = P(A)+1/5

P(A)=3/4 - 1/5

P(A)=(15-4)/20

= 11/20

Therefore, P(A)=11/20

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