the blueprints at addison circle is a sculpture that took 18,000 worker-hours to construct using over 410,000 pounds of steel. The piece of art is placed within a traffic circle with a diameter of 133 feet. find the area of the circle. Round to the nearest tenth of a square foot.

Answer: ZR and ZS form a right angle

Step-by-step explanation:

Complementary angles are angles whose sum = 90ᴼ

If R and S are complementary, then their angle measures add to equal 90ᴼ

A right angle = 90ᴼ

ZR and ZS form a right angle.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

When two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection, they form the right angle.

According to the given question.

Angles R and S are complementary angles.

Since, R and S are complementary angles. then their angle measured add to equal to 90 degrees or right angle.

Therefore,

The ZR and ZS form a right angle.

Hence, option second is correct.

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Answer:

120

Step-by-step explanation:

To solve this, we can first find the value of the number.

Let's name the number x.

We can set up a proportion to solve.

90/60=x/100

Simplify.

9/6=x/100

Cross multiply.

6x=900

Divide both sides by 6.

x=150

The original number is 150.

Let's find 4/5 of that.

4/5*150

Multiply.

600/5

Divide.

120

________________________________

Hey!!!

Solution,

Let the number be X

60% of X=90

or,60/100*X=90

or,3/5*X=90

or,X=90/3/5

or,X=90*5/3

or,X=450/3

X=150

Again,

4/5 of X

=4/5*150

=120

The answer is 120

hope it helps

Good luck on your assignment

_____________________________

Answer:

Millionths

Step-by-step explanation:

It is the fartherst decimal place that thier is.

Answer:

340 songs, 17000/50 = 340 lol

Answer:

340

Step-by-step explanation:

17000÷50=340.

hope this helps

Answer:

7.809 g/cm^3

Step-by-step explanation:

Density is mass over volume so we need to find the mass and volume of the steel.

First we find the volume of the wood:

Vw = 9*6*6 = 324 cm^3

now we can find the mass of the wood, as mass = density * volume

mw = .68*324 = 220.32g

subtracting the mass of wood from total mass, we get the mass of steel

970-220.32 = 749.68g

now we can find the volume of the pyramid

Vs = 1/3 *6*6* (17-9) = 96 cm^3

Now we divide mass by volume to get density

749.68/96 = 7.809 g/cm^3

Confirming this with known data, density of steel is roughly between 7.75 and 8.05 g/cm^3 so we know we're correct.

Answer:

9x^2 +12x

Step-by-step explanation:

To find the area of a rectangle you need to multiply the length by the width. So,

3 by 3x^2 = 9x^2

3 by 4x = 12x

So the area of the entire rectangle is: 9x^2 + 12x

Answer:

C

Step-by-step explanation:

Constant means unchanging. You can see that there is a portion in the graph where the line is just flat. That means that the graph is constant in that interval. Find where the constant line starts and ends. Since the coordinates are increasing by 2, and the constant line starts between 0 and the first tick (2), the constant line starts at 1. Do the same thing to find where it ends(the last point where the line is flat). This should be 6.

That means the line is unchanging(constant) from 1 to 6, which can be represented by C.

Answer: x=-0.792

Step-by-step explanation:

For this problem, you want to get like terms onto one side, then solve for x.

[tex]\frac{1}{25}=5x+4[/tex]

[tex]-\frac{99}{25} =5x[/tex]

x=-0.792

Answer:

5(4x + 5)

Step-by-step explanation:

Given

20x + 25 ← factor out the common factor 5 from each term

= 5(4x + 5)

Answer:

5(4x+5)

Step-by-step explanation:

divide both with the same number into smallest digit

eg: 5(4x+5)=20x+25

if 5x4=20 and 5x5=25

both can be divided by 5 to get smallest number(factorise it)

The complete question is:

A certain element has a half life of 4.5 billion years.

You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock?

Answer:

Age of rock = 7.82 billion years

Step-by-step explanation:

For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.

We are given that;

fraction remaining = 30% = 0.3

Thus;

0.3 = 0.5n

To find n, we have to use the log function;

log 0.3 = n log 0.5

-0.5229 = -0.301 n

n = -0.5229/-0.301

n = 1.737

We are given that;

Half life = 4.5 billion years

So, 1.737 half lives would give;

1.737 × 4.5 = 7.82 billion years

So, age of rock = 7.82 billion years

Answer:

-7/4

Step-by-step explanation:

((5 + 1)^2- (11 +32))/ 4=(36-43)/4= -7/4

Answer:

31

Step-by-step explanation:

I assume you meant h(t) = 160t - 16t^2, as h(t) = 160t - 16t2 has no maximum.

There's two ways of solving this:

(i) By completing the square and finding the maximum turning point.

(ii) By using Calculus methods to find derivative and equating it to 0 in order to find maximum turning point.

(i) h(t) = 160t - 16t^2

h(t) = -16t^2 +160t

h(t) = -16(t^2-10t) (by taking out a common factor of -16)

h(t) = -16[(t-5)^2 - 25] (by completing the square)

h(t) = -16(t-5)^2 + 400 (on multiplying out by -16)

From this we see that the turning point is at (5;400), therefore the maximum height is 400 feet and is reached after 5 seconds.

Or...

(ii) h(t) = 160t - 16t^2

h`(t) = 160 - 32t (where h`(t) = derivative of h(t))

Now to find maximum of h(t), we set h`(t) = 0 and solve for t:

0 = 160 - 32t (on substituting h`(t) = 0)

32t = 160 (on solving for t)

t = 160/32 (on dividing both sides by 5)

t= 5

Now we have found that at 5 seconds, we will reach our maximum height. So to find this maximum height, we'll have to substitute t=5 into h(t) = 160t - 16t^2.

h(5) = 160(5) -16(5)^2

h(5) = 800 - 400

h(5) = 400 feet

So, once again we have shown that maximum height is 400 feet and is reached after 5 seconds.

Answer:

0,-11

Step-by-step explanation:

-p^2 − 11p = 0

Factor out -p

-p( p+11) =0

Using the zero product property

-p =0    p+11 =0

p =0      p = -11

Let's see if we can recreate the histogram from the description.

Time count

0.5  0

1       0

1.5    2

2      1

2.5   3

3       1

3.5    2

4       1

4.5    0

5       0

The mean is between 2.5 and 3 so that will definitely decrease with a data point that's less that that, as 0.5 is.  

For 10 data points the median is the average of the 5th and 6th when sorted, and those are both 2.5.  When the new point is added the median will be the 6th of 11 points, still 2.5 in this story.

Answer: B  the mean will decrease

Answer:

B

Step-by-step explanation:

This is because the mean will decrease

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

This is the distance formula. To find the distance, solve as shown:

[tex]d=\sqrt{(6-9)^{2}+(3-(-2))^{2} } \\d=\sqrt{(6-9)^{2}+(3+2)^{2} } \\d=\sqrt{(-3)^{2}+(5)^{2} } \\d=\sqrt{9 +25 } \\d=\sqrt{34 }[/tex]

Answer:

The roots are real and unequal (3, -3)

Step-by-step explanation:

x²-9=0

ax²+bx+c=0

Comparing we get,

a= 1

b= 0

c = -9

Determinant: b²-4ac

= 0² - 4(1)(-9)

= 36>0

D > 0

Therefore, the equation has real and unequal roots.

Algebraic identity:

x² - a² = (x-a)(x+a)

Using this identity

x²-9 = (x+3)(x-3)

Roots are 3 and -3 which are real and not equal to each other

Hope this answer helps you ..

Answer:

2 real solutions

Answer:

(4 , 3 ) and (-3 , -4)

Step-by-step explanation:

Other two vertices will be in 1st quadrant and 3 rd quadrant

Answer: (4 , 3 ) and (-3 , -4)

Step-by-step explanation: Other two vertices will be in 1st quadrant and 3 rd quadrant

Answer:

144cm²

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The parent graph of this function is the absolute value, or |x|. However, it is shifted 8 units to the right and 2 units up. Therefore, the equation of this function is y=|x-8|+2, or answer choice C. Hope this helps!

Answer:

-8 and 4

Step-by-step explanation:

4x = 32 -x^2

Subtract 4x from both sides and rearrange the equation:

-x^2 -4x +32 = 0

Use the quadratic equation x = -b +\ - sqrt(b^2-4ac)/ 2a

From the rewritten equation: a=-1, b = -4 and c = 32

Solving for x you get x = -8 and x = 4

The solutions are -8 and 4

Answer:

1) a²-9a+20

2)a²-12a+20

3)a²+a-20

4)a²-8a-20

Step-by-step explanation:

use (foil)

front

outside

inside

last

Answer:

[tex]f(x)=-3x^2[/tex]

Step-by-step explanation:

A quadratic function is a function in which its degree (Highest power of the variable) is 2.

[tex]f(x)=-3x^2[/tex] is the function that has a degree of 2.

Step-by-step explanation:

Isosceles means that two sides are equal.

if the base is 1½s the other two sides will be ½s and½s

thus perimeter=1½+½+½ =2½s

smaller triangle:

perimeter=½(1½s+½s+½s)

=½(2½s)

=1¼s convert to decimal

=1.75s

The simplified expression of the given situation is 1.75s.

The correct option is C.

A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.

Given:

The base of an isosceles triangle is one and a half times the length of the other two sides.

Let s represents the side of the triangle.

The base = ([tex]1\frac{1}{2}[/tex])s = 3s/2

So, the other two sides are s and s.

So, the perimeter,

= 3s/2 + s/+ s

= 7s/2

A smaller triangle has a perimeter that is half the perimeter of the first.

That means,

the perimeter of the smaller triangle,

= 1/2(7s/2)

= 7s/4

= (1.75)s

Therefore, (1.75)s is the required expression.

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Answer: 3 3√3

Step-by-step explanation:

81^1/3

=3√81

= 3 3√3

Answer:

Option D

Step-by-step explanation:

because the data wasn't place on a table...

Answer:

C

Step-by-step explanation:

5×2=10

10-15x-20

-10-15x

5(-2-3x), or -5(x+4)(x-1) solve it and find your answer

Answer:

0.2666666667

Step-by-step explanation:

Answer: 384 miles

Step-by-step explanation:

From the question, Mrs. Schroeder, a school principal, drove her own car for a class trip, by taking a different route and we are told that the principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip.

Since it used 1 gallon of gas for 32 miles, 12 gallons will be for:

= 32miles × 12

= 384 miles

The principal drove for 384 miles.

Answer:

three angles of a polygon are each 105.5,the sum of the angles in the polygon is 2520. find each of the other angles if they are equal to each other. For a polygon with n sides and n angles, the sum of the measures of all the interior angles equals (n-2)180 degrees. 16-3=13