x=? y=? (Show work)

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

vertex= (4,-5)

Step-by-step explanation:

find the x and y values on the equation by solving

x= -56/2(-7) and y= -7x^2+56x-117

Answer:

I'm pretty sure the number of stamps purchase is about 132 stamps

The dot isn’t shaded so > or <

From -55, it’s showing small than

From -49, it’s showing greater than

x < -55 or x > -49

Answer:  x < -55 or x > -49

Step-by-step explanation:

x < -55 or x > -49

They both start with an opened circle, and also these two opened circle dots do not connect to each other. On the left side, the number is going from -55 to the smaller side, -57 or less, so we can say that x is smaller than -55. On the right side, the number goes from -49 to the bigger number, we can say that x is greater than -49.

Answer:

10

Step-by-step explanation:

4 times 3 = 12

12-2=10

a. 132:89

b.132 to 89

c.132:14

b. 132 to 14

The polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

To simplify a mathematical expression is to represent it in the least complicated form possible.

In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

The given expression;

= (3x²- x - 7) - (5x² - 4x - 2) + (x + 3)(x + 2)

The simplified form of the given expression is calculated as follows;

= 3x² - x - 7 - 5x² + 4x + 2 + x² + 2x + 3x + 6

= -x² + 8x + 1

Thus, the polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

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a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

Answer:

c + 11 = 43

Step-by-step explanation:

C = Carlos age

11 = The number added

43 = The number added plus carlos' age

c +11 = 43

c = 43 - 11

c = 32

Carlos' age is 32 years.

Answer:

C+11=43

Step-by-step explanation:

C= Carlos age

11= added number

43= Carlos age +added number

C+11=43

C=43-11

C=32

Age of Carlos 32.  :)

Possible Answers:

y = 1/4x + 17

y = -4x + 17

y = 3x + 5

y = 4x - 17

Correct answer:

y = -4x + 17

Explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Answer:

V =704 m^3

Step-by-step explanation:

Remark

The Volume of a cubical Prism = Length * Width * Height of L * w * h

Givens

L = 22 meters

w = 4  meters

h = 8 meters

Solution

V = L * w * h

V = 22 * 4 * 8

V = 704 m^3

What is the volume, in cubic meters, of a rectangular prism that has a length of 22 meters, a width of 4 meters, and a height of 8 meters?

In this question we are provided with the length, breadth and height of a rectangular prism. We are asked to calculate the volume of the rectangular prism.

We know,

\( \star \: \small\boxed{ \rm{ Volume_{(rectangular \: prism)} = L×B×H}}\)

Where,

Substituting the values we get

\( \small\sf{ Volume_{(rectangular \: prism)} = 22×4×8 = 704 m³}\)

Hence, the volume of the rectangular prism is 704 m³.

Answer:

monthly payment = $918

interest payment = $450

principal payment = $468

new loan balance = $119,532

Step-by-step explanation:

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

Answer:

Step-by-step explanation:

The milepost number of the rest area is 7 miles away from milepost 58, so it can be represented by the equation:

m = 58 + 7

This equation states that the milepost number of the rest area is equal to 58 plus 7, or 65. Therefore, the rest area can be located at milepost 65.

Answer:

18

Step-by-step explanation:

you will use multiplication

3(packages of pencils)×6(pencils)=18pencils

so she will need 18 erasers for each pencil

He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

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The rectangle that is shaded has an area of 18 square units.

The framed rectangle is represented by the darkened area, while the frame is shown in white.

The frame's known width is two units, and both the rectangle and the frame have the following dimensions:

width = 7 units

length = 10 units

Now, if we remove the frame, each measure will lose 2*2 units, or 4 units (because for each measure we have the frame in both sides).

As a result, the measurements for the shaded rectangle are as follows:

width = 7 units - 4 units = 3 units

length = 10 units - 4 units = 6 units.

And since the product of a rectangle's width and length determines its area, we may calculate:

A = (3 units)*(6 units) = 18 square units.

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Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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Answer:

First option

Step-by-step explanation:

Common ratio is greater than 1

Answer:

rounded 71.2%

Step-by-step explanation:

4200/5900 * 100 = 71.186440678

rounded 71.2%

Answer:

Option B

\( \frac{p - 1}{b} \)

Step-by-step explanation:

\(p = i + hb \\ p - i = hb \\ divide \: both \: sides \: by \: b \\ \frac{p - i}{b} = \frac{hb}{b} \\ \frac{p - i}{b} = h\)

Answer:

Step-by-step explanation:

Substituting he coordinates:

Answer:

Product for A = 046

Product for B = 0230

Sum for C = 0.0276

Step-by-step explanation:

We need to multiply the terms and find the answers

First we multiply 2 with 0.23, then we multiply 1 with 0.23

   0.23

x    0.12

-------------

     046

   0230

--------------

    .0276

Since there are 2 numbers after decimal in 0.23 and same for 0.12, so we place the decimal so that there are 4 decimal places.

Counting of decimal will start from the units place.

So, Product for A = 046

Product for B = 0230

Sum for C = 0.0276

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).

In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.

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The quotient of the given expression is 68.

What is the quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

For the given problem,

To find out the estimation of the quotient, we first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient.

Given, 3411 divided by 53

So, the rounding value becomes 3400 divided by 50,

then, 3400/50 = 68

Hence, the quotient is 68.

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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