The Golden Ratio appears in the design of the Greek Parthenon because the width and height of the façade are related by the equation [tex]\frac{W+H}{W} = \frac{W}{H}[/tex]. If the height of a model of the Parthenon is 16 inches, what is its width? Round your answer to the nearest tenth.

Answer:

Third zero is -1.

Step-by-step explanation:

consider the given polynomial is  

[tex]P(x)=x^3+5x^2+7x+3[/tex]

It is given that -1 and -3 are two zeroes, therefore (x+1) and (x+3) are two factors of given polynomial.

The given polynomial can be rewritten as

[tex]P(x)=x^3+x^2+4x^2+4x+3x+3[/tex]

[tex]P(x)=x^2(x+1)+4x(x+1)+3(x+1)[/tex]

[tex]P(x)=(x+1)(x^2+4x+3)[/tex]

Now, splitting the middle term, we get

[tex]P(x)=(x+1)(x^2+3x+x+3)[/tex]

[tex]P(x)=(x+1)(x(x+3)+1(x+3))[/tex]

[tex]P(x)=(x+1)(x+1)(x+3)[/tex]

[tex]P(x)=(x+1)^2(x+3)[/tex]

Here, power of (x+1) is 2. It means the multiplicity of zero -1 is 2.

So, three zeroes are -1, -1 and -3.

Therefore the third zero is -1.

Answer:

Let humans be x and horses be y

Both have one head each,so x+y=74 (1)

Humans have 2 legs each and horses 4 legs each…… so 2x+4y=196 (2)

In first equation x+y=74 then y=74~x (3) ……… .By solving both equations we have as under… x+3y=122 x=122-3y (4)…. Now in equation 4 we put the value of y taken from equation 3 so it will be x=122~3(74-x)…. x=122-222+3x…………. bringing x on one side x-3x=122~222 therefore -2x=~100….. x=50… put the value of x in first equation… x+y=74… 50+y=74… y=74~50…..… y=24… Now it is concluded that Humans are 50 and Horses are 24.. Now you put the values of x & y in 1st and 2nd equation … you will get x+y=74.. 50+24=74………..2x+4y=196…2×50+4×24=196.. it is proved thru equation.

Answer:

need points sorry

Step-by-step explanation:

Answer:

The baby grows at an average of 1.5 pounds each month.

Step-by-step explanation:

I got this correct on my quiz.

Answer:

A.

3x + 3y = 0

7x − y = 8

Step-by-step explanation:

Given

3x + 3y = 0

-4x + 4y = -8

Required

Find the equivalent

To solve for the equivalent we simply solve for x and y in the given equation.

Subtract 3x from both sides in 3x + 3y = 0

3x - 3x + 3y = 0 - 3x

3y = -3x

Multiply both sides by ⅓

⅓ * 3y = -3x * ⅓

y = -x

Substitute -x for y in -4x + 4y = -8

-4x + 4(-x) = -8

-4x -4x = -8

-8x = -8

Multiply both sides by -⅛

-⅛ * -8x = -⅛ * -8

x = 1

Recall that y = -x

y = -1

So, we have that x = 1 and y = -1

We'll substitute these values in the list of options;

A.

3x + 3y = 0

7x − y = 8

7(1) - -(1) = 8

7 + 1 = 8 ----- This is equivalent

B.

3x + 3y = 0

−7x − y = 8

-7(1) - (-1) = 8

-7 + 1 = 8

-6 ≠ 8 .... This is not an equivalent expression

C.

3x + 3y = 0

−7x + 7y = 8

-7(1) + 7(-1) = 8

-7 -7 = 8

-14 ≠ 8 .... This is also not an equivalent expression

D.

3x + 3y = 0

-4x + 7y = 8

-4(1) + 7(-1) = 8

-4 -7 = 8

-11 ≠ 8 -_- This is also not an equivalent expression

Answer:

A is the correct one

Step-by-step explanation:

Answer: The answer is "experiment."

Step-by-step explanation:

This procedure is being used in order to validate a hypothesis, particularly in a research study. In the situation above, you have to validate whether a new reading program can increase reading comprehension or not.

The experiment consists of independent, dependent, and controlled variables. The independent variables are the ones being changed by the researcher, while the dependent variables tell whether the changes in the independent variable is significant. The controlled variables are the ones that are constant.

The dependent variable above is reading comprehension, while the new reading program is the independent variable. Examples of controlled variables are the ages of the participants. The age directly affects the reading comprehension, thus it has to be considered.

Answer:

A.

Step-by-step explanation:

[tex]\sqrt{10} *\sqrt{8}\\ \sqrt{10}*\sqrt{2*4}\\\sqrt{10}*2\sqrt{2}\\2\sqrt{2*10}\\2\sqrt{20}\\ 2\sqrt{4*5} \\4\sqrt{5}[/tex]

Answer:

Quadrant 2

Step-by-step explanation:

The answer is quadrant two because the answer is in the form of -x,y. When the x is negative and the y is positive, it is always going to be in quadrant 2. As you can see in the image below, quadrant 1 is going to be all positive, quadrant two is going to be negative then positive, quadrant three is going to be all negative, and quadrant 4 is going to be positive then negative. Use this as a guide for the rest of your question. I hope this helps!

Answer:

y = (-1/2)x - 3

Step-by-step explanation:

The line y = 2x - 6 has a slope of 2 and so any line perpendicular to it has a slope which is the negative reciprocal of 2:  -1/2.

If this perpendicular line passes through (0, -3), then the slope-intercept equation y = mx + b becomes -3 = (-1/2)(0) + b, or -3 = b, and the desired

equation is

y = (-1/2)x - 3

Answer: 22.4

Step-by-step explanation:

The distance formula can be used to solve this problem.

[tex]D=\sqrt{(x_{2}-x_{1} )^2+(y_{2}-y_{1} )^2}[/tex]

We can plug in our x and y values to find the distance.

[tex]D=\sqrt{(14-4)^2+(-11-9)^2}[/tex]

[tex]D=\sqrt{10^2+(-20)^2}[/tex]

[tex]D=\sqrt{100+400}[/tex]

[tex]D=\sqrt{500}[/tex]

[tex]D=22.4[/tex]

Our distance between the points is 22.4.

Answer:

Answer:

18 cups.

Step-by-step explanation:

We are given that Bernie spends $6.50 on ingredients and cups for his lemonade stand. He charges $1.50 for each cup of lemonade. Inequality that represents this situation: .

To find number of cups x to make a profit of at least  $20 we will use our given inequality.

Therefore, in order to make a profit of at least $20 Bernie need to sell 18 cups of lemonade.

Answer:

this the right answer

Step-by-step explanation:

18, 23

Answer:

D). 19

Step-by-step explanation:

When you subtract

7 - 26 = 19

26 - 45 = 19

45 - 64 = 19

64 - 83 = 19

The common difference is 19

Answer: C. (1, 4)

Step-by-step explanation:

The point where the two lines meet or intersect is the solution to the system of equations graphed. And in this case, the lines intersect at (1, 4).

Answer:

the 2nd choice

Step-by-step explanation:

-2 1/4  ÷  (-2/3)= - 9/4 ÷ (-2/3)

Answer:

D. plane

Step-by-step explanation:

A. is incorrect because three points don't make a point.

B. is incorrect because all points in a ray are colinear.

C. is incorrect because the three points are not colinear.

D. is correct because, for a given three different points, there is a plane that contains them.

Answer:

D

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

We need to find a pair of lines that represents the equations with the solution (4, −1).

Since (4,-1) is the solution of the equations. It means (4,-1) is the intersection point of lines.

4 on x-coordinate means 4 units right.

-1 on y-coordinate means 1 unit down.

A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the right and 1 unit down.  

Therefore, the correct option is B.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function

[tex]C(x) = 1000 +5.70x + 7x^2[/tex]

To get the instantaneous rate of change with respect to x, when x= 100

we have to substitute x= 100 in the given function and solve.

we have

[tex]C(x) = 1000 +5.70(100) + 7(100)^2\\\\C(x) = 1000 +5.70(100) + 7(100)^2\\\C(x)= 1000+570+7*10000\\\\C(x)= 1570+70000\\\\C(x)= 71570[/tex]

Answer: 159.7

Step-by-step explanation:

Answer:

UV and WV

Step-by-step explanation:

Answer:

a- 6/18 or 1/3

 the number of red counters/ the total number of counters

b-14/18 or 7/9

 the number of counters that are not blue/ the total number of counters

good luck

Answer:8

Step-by-step explanation:area of the triangles is each 2 and the square is 4

Answer:

8 units²

Step-by-step explanation:

we have a trapezium

A = (b+B)×h/2

b = 2

B = 2+2+2 = 6

h = 2

A = (2+6)×2/2 = 8 units²

Answer:

V =1620 pi  cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi ( 9)^2 * 20

V =1620 pi  cm^2

Answer:

1) x=70

2) x=70

3) x=155

4) x=24

5) x=40

Step-by-step explanation:

1) 180-105=75

alternate interior tells us the top will be 35

180-75-35=70

2) Alternate interior tells us the second angle in the first triangle = 60

180-50-60=70

3) The third angle in the top triangle is found by 180-90-35=55

Using this we can find the top angle of the bottom triangle by 180-60-55=65

Then we can find the bottom angle of the bottom triangle with 180-65-90=25

This means that x=180-25=155

4) The bottom angle on the right is 180-94-41=45

That means that x=180-111-45=24

5) x=180-50-90=40

Answer:

X=36

Step-by-step explanation:

3x+72=180

3x=180-72

3x=108

x=36

Answer: 2 <= X <= 5

Step-by-step explanation:

Given that a factory can work its employees no more than 5 days a week, that is, less than or equal to 5 days.

And no less than 2 days per week. That is, greater than or equal to 2 days.

Let X be the number of days employee can work. Then, according to the first statement, X <= 5 and according to the second statement, X >= 2

An inequality to represent the range of days an employee can work will be

2 <= X <= 5

Therefore, an employee can work for 2 days, 3 days, 4 days and 5 days

Short Answer:

1. C ( 60 degrees)

2. B (90 degrees)

Explanation:

The first one is 60 degrees, because every 5 minutes the minute hand goes 30 degrees and she took 10 minutes.

30 x 2

=60 degrees

The second one is 90 because one section is 30 degrees. so,

30 x 3

= 90 degrees

Hope this helps :)

Answer:

A. III only

Step-by-step explanation:

In mathematics, an identity is one of the characteristics of algebraic expressions.

Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.

Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.

In the above question, we are given 3 Options.

I) 3(5 + 2x) = 15 + 6x

II) y = x + 3

III) (x² - y²) = (x + y) (x - y)

Option I) 3(5 + 2x) = 15 + 6x

Is showing distributive property in mathematics.

Distributive property is :

a(b + c) = ab + ac

Option I is not an identity , therefore it is wrong.

Option II) y = x + 3 is just an algebraic expression.

Only Option III is an identity. This is because it follows the rule of

(a² - b²) = (a + b) (a - b)

We can prove and confirm this be solving the algebraic expression

(x + y) (x - y)

We expand the bracket

x² - xy +xy - y²

x² - y²

Therefore, option A is the correct option.

Answer:

Step-by-step explanation:

Lets start by defining the numbers in the equation.

This  equation is in slope-intercept form meaning that it is y=mx+b or y = b+mx they are both the same

In slope-intercept form,

Th equation is y=400+32x so now we know

For the first question the change per minute is the rate so it is 32.

For the second question the starting amount is the same as the y-intercept so it is 400.

Answer:

C

Step-by-step explanation:

A. (4, 0) and (4, 3) have the same x coordinate (Can't happen in a function).

B. (2, 5) and (2, 1) have the same x coordinate.

C. It passes the vertical line test on a graph and no x is repeated.

D. (2, 3) and (2, 5) share the same x coordinate.

Answer:

c is correct answer.

a function from set A (x coordinate) to set B (y coordinate) a special type of relation defined from set A to set B if every element of set A is mapped with unique element of set B.

Answer:

11 gallons

Step-by-step explanation:

We can set up a proportion.

g represents gallons of punch.

24/144=g/66

We can simplify the left side:

1/6=g/66

We cross multiply.

6g=66

g=11

You need 11 gallons of punch to serve 66 guests!