In the figure below, Z is the center of the circle. Suppose that QR=4x-2, SR=10, ZU=8, and ZV=8. Find the following.
Z
W
VS =
0
8 08
X
S

Answer: It would be A, 12.28 degrees.

Step-by-step explanation: Remember the acronym for sin cos tan, SOH CAH TOA. Where s c and t stand for sin cos tan, and the A stands for adjacent side, O stands for the opposite, and H stands for the hypotenuse. Here, side AC is opposite to the angle 17 degrees, and we have the measure of the hypotenuse side. So plug in accordingly, sin 17 = x /42. Use any variable for the unknown side. Multiply 42 to sin 17 to get 12.279, which rounds to 12.28 degrees. Make sure your calculator is in degree mode, since we are dealing with degrees.

The equations that can be used to determine the length of the room are:

y(y + 5) = 750

y²– 5y = 750

(y - 30) (y + 25) = 0

A rectangle is a two-dimensional object that has four sides and four right angles. The sides of a rectangle are known as the width and the length.  A rectangle has two diagonals of equal length which bisect each other at right angles.

Area of a rectangle = length x width

750 = y x (y - 5)

750 = y² - 5y

y² - 5y - 750 = 0

The factors of -750y² that add up to -5y are 25y and -30

(y² + 25y)(-30y - 750) = 0

y(y + 25) = 0

-30(y + 25) = 0

(y - 30) (y + 25) = 0

Here is the complete question:

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

Answer: Delete the point (0, 4)

Step-by-step explanation:

Your line for y = (1/3)x + 4 is correct.

                             m=1/3   b=4

Start at (0, 4) and draw a line through a point up 1 and 3 to the right (3, 5).

Your line for x = 6 is correct.

A vertical line through (6, 0), (6, 1), (6, 2), ...

Your point for (6, 6) is correct.

                    x=6, y=6

Your error is that you used the dot tool to plot a point for (0, 4). You DO need this point to create the line y = (1/3)x + 4, however the instructions do not state to mark this coordinate with a dot.

Area is length x width:

4x^3y^2 x 3x^2y^3

Apply the exponent rule: a^b x a^c = a^(b+c)

4 x 3 = 12

x^3 x x^2 = x^5

y^2 x y^3 = y^5

Combine for final answer: 12x^5y^5

The approach for solving for incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.

It can also be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Formula for solving incenter:

Let (x1,y1) , (x2,y2) and (x3,y3) are three points of triangle.

and a,b,c are lengths of sides.

I = ((ax1+bx2+x3 / a+b+c  ,  ay1+by2+cy3 / a+b+c))

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

In order to write log10(0.001) = -3 in index form, we have \(10^{-3} = 0.001\).

The logarithm of a number refers to the power to which a given base is raised to give the number. In this case, the base is 10 and the index is 3. Our task is to write log10(0.001) = -3 in index form.

Recall that;

Hence, to write  log10(0.001) = -3 in index form we have to write, \(10^{-3} = 0.001\)

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Answer:

7n-13

Step-by-step explanation:

Simplify

4n+3(n-5)+2

4n+3n-15+2

Add The Numbers

4n+3n-15+2

4n+3n-13

Combine Like Terms

4n+3n-13

7n-13        Solution 7n-13

Answer: we need to survey 2285 Americans.

Step-by-step explanation:

When population proportion (p) is known, then the formula to evaluate the sample size( minimum) is given by :-

\(n=p(1-p)(\frac{z^*}{E})^2\), where E = margin of error , z* = critical z-value.

Given: p= 0.61, E=0.02, Critical z value for 95% = 1.96

Required sample size: \(n=(\frac{1.96}{0.02})^2(0.61)(1-0.61)\)

\(=(98)^2(0.61)(0.39)\\\\=9604(0.61)(0.39)\\\\\approx$$2285\)

Hence, we need to survey 2285 Americans.

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

The formula for the circumference is C = 2*pi * r

Givens

r = 50 feet

pi = 3.14

Solution

C = 2* 3.14 * 50

C = 314 feet

So one turn of the ferris wheel would allow a person to travel 314 feet around the circle.

The equation that best describes the relation is y = -x+1 ( optionD)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Taking x(0,1) and y ( 1,0)

therefore the slope of the line

= 0-1/1-0

= -1/1 = -1

the equation a line is given as

y-y1 = m(x-x1)

= y-1 = -1( x - 0)

= y-1 = -x

y = -x +1

therefore the equation that describe relation is y = 1-x or y = -x+1

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Answer:

-1/2, or -0.5

Step-by-step explanation:

Slope = delta y/delta x

In this situation, you would do.

0. 5 - 1 / 0.25 - (-0.75)

0.5 - 1 = -0.5

0.25 -(-0/75) = 1

-0.5 / 1 = slope

-0.5 = slope

or

-1/2 = slope

Hope this helps!

Answer:

x = - 3/7

y = - 8/7

Step-by-step explanation:

(2x - 6y = 6)/2 =

x - 3y = 3

x = 3y + 3

Substitution:

6 (3y +3) - 4y = 2

18y + 18 - 4y = 2

14y = -18+2

y = -16/14

y = - 8/7

Substitution:

x = 3(-8/7)+3

x = -24/7 + 3

x = -3/7

9514 1404 393

Answer:

  (x, y) = (-3/7, -1 1/7)

Step-by-step explanation:

We can divide each equation by 2 and subtract the constant to put them in general form.

  x -3y -3 = 0

  3x -2y -1 = 0

This form facilitates use of the "cross multiplication method" of solution. That method tells us ...

  1/d1 = x/d2 = y/d3

where the differences d1, d2, d3 are the differences of cross-products:

  d1 = 1(-2) -(3(-3)) = 7

  d2 = -3(-1) -(-2(-3)) = -3

  d3 = -3(3) -(-1(1)) = -8

Then the solutions are ...

  x = d2/d1 = -3/7

  y = d3/d1 = -8/7

(x, y) = (-3/7, -8/7)

_____

Additional comment

When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)

The pattern in the cross-differences is relatively easy to see:

The expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.

Answer:

6035ft

Step-by-step explanation:

Given data

Length=x

WIdth= 6x^3 + 1 − x^2

The expression for the perimeter is given as

P= 2L+2W

substitute

P=2(x)+2(6x^3 + 1 − x^2)

open brackets

P=2x+12x^3+3-2x^2

rearrange, the polynomial that models the perimeter of the rectangle is

=12x^3-2x^2+2x+3

Also, the perimeter when length x= 8 is

P=12x^3-2x^2+2x+3

P=12(8)^3-2(8)^2+2(8)+3

P=12*512-2*64+16+3

P=6144-128+19

P=6016+19

P=6035 feet

Hence the perimeter of the rectangle is 6035ft

None of the chosen pairs will be dependent as nothing is specified.

Independent events are those events whose occurrence does not have any effect on the events that may occur or occurred.

Dependent events are those vents whose occurrence either depends on some other event or has an effect on occurring or occurred vents.

Given, The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.

As not mentioned that what kind of book he chooses first or types of book.

Also which shelf he chooses first choosing the first book is independent

and choosing the second book is also independent so none of the chosen pair will be dependent.

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Answer:

Q13)A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages. Present age of the father is = 4 x = 4 × 10 = 40 4x=4\times10=40 4x=4×10=40 years.

In mathematics, the term "difference" is commonly associated with subtraction. Subtraction is an arithmetic operation that involves finding the difference between two numbers or quantities.

When we subtract one number from another, we are essentially finding the difference between them. The result of a subtraction operation is called the difference. For example, in the expression 10 - 5, the difference is 5, indicating that the number 5 is the result of subtracting 5 from 10.

Subtraction is denoted by the minus sign "-" or by using the word "minus" or "subtract" in mathematical expressions. For instance, in the equation 8 - 3, we are subtracting 3 from 8 to find the difference.

The concept of difference is fundamental in various mathematical applications. It allows us to compare quantities, measure distances, determine changes, and solve various problems. For instance, when analyzing data sets, we often calculate the differences between values to understand patterns, trends, or changes over time.

The difference between two numbers can be positive, negative, or zero. If the minuend (the number from which subtraction is performed) is greater than the subtrahend (the number being subtracted), the difference is positive. If the subtrahend is greater, the difference is negative. When both numbers are equal, the difference is zero.

For example, in the subtraction 7 - 3, the difference is 4. In the subtraction 5 - 9, the difference is -4. And in the subtraction 6 - 6, the difference is 0.

Overall, the concept of difference is a crucial aspect of subtraction, providing a measure of the numerical distance between two quantities. It allows us to express the result of a subtraction operation and plays a significant role in various mathematical calculations and analyses.

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Therefore , the solution of the given problem of linear equation comes out to be the decision variables x1, x2, x3, and x4 must be non-negative.

The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to as a "simple algorithm incorporating many factors" even though the section before it includes independent parts. Bivariate linear equations only contain two variables. Application problems with linear equations have no known answers. Y=mx+b, also known as mx+b, provides a number of straightforward equations.

Here,

To solve this linear programming problem, we can use the following decision variables:

Let x1 = number of pancakes

Let x2 = number of eggs

Let x3 = number of sausage patties

Let x4 = number of slices of toast

The objective function is to minimize cost:

Minimize Z = 0.5x1 + 0.2x2 + 0.3x3 + 0.1x4

Subject to the following constraints:

Calories: 120x1 + 90x2 + 280x3 + 70x4 >= 420

Iron: 1.2x1 + 1.8x2 + 2.4x3 + 0.8x4 >= 5

Calcium: 10x1 + 20x2 + 90x3 + 20x4 >= 400

Protein: 3x1 + 6x2 + 9x3 + 3x4 >= 20

Fiber: 2x1 + 0.5x2 + 1x3 + 1x4 >= 12

Fat: 2x1 + 6x2 + 20x3 + 1.5x4 <= 20

Cholesterol: 50x1 + 190x2 + 60x3 + 0x4 <= 30

The decision variables x1, x2, x3, and x4 must be non-negative.

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With help of integration, The volume of the  solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16 will be 42.66 cubic unit.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

for volume of the   solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16.

volume= ∫√x dx for x=0 to 16

=x*√x/3/2

=64*2/3

=128/3

=42.66 cubic unit

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Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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Answer:

is this a test > : (

Step-by-step explanation:

Answer:

f

Step-by-step explanation:

Four points are always coplanar if they: lie in same plane.

Firstly understanding the coplanar points. Coplanar points are refers to the points if they are present in same plane. Further defining the word "plane". Plane is the surface, which is flat and two dimensional in nature. The surface is infinite. Plane can also be referred as the analogue of 3 dimensional space, you we can also interpret the plane as extension of point or line.

So, the points that lie on different planes will not be coplanar. Now, understanding the points on lines. Two or more lines may or may not be in same plane. Subsequently, points may or may not be coplanar, depending upon the lines they are placed on. Thus, we can not definitely say that points lying on the same line are coplanar.

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Answer:

Step-by-step explanation: There are different methods to solve this, but I chose to change these into decimals- 1.8 and .20, to make it easier. Since miles per hour is speed, and speed is distance divided by time, all you have to do is fill in the blanks.

Since 1.8 / .20= 9, the answer is 9 miles per hour.

To take it a step farther, you could multiply this by any number of hours, or convert it to minutes. For example, to figure out how far they'd get in 10 minutes, I could divide the unit rate by 60, since there are 60 minutes in an hour, and get 0.15. So, in 10 minutes, they'd get 0.15 miles away.

Just in the mood for math, ig.

Ew, did I just say that? >.<

Answer:

8 significant figures should be provided.

Step-by-step explanation:

I believe I am correct, but check your answer anyways.