A Roman statue is three times as old as a Florentine statue. One hundred years from now the Roman statue will be twice as old as the Florentine statue. How old is the Roman statue?

Answer:

the answer is c

Step-by-step explanation:

when expanded the first three coefficients are 1 4 6

Answer:   CCCCCc

1,4 and 6

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

According to the graph it never crosses the x axis meaning that it has 0 roots beecasue roots is another word for x-values.

Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.

The area of the figure decreases when the dimension is decreased

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the figure be represented as ABCD

where ABCD is a rectangle

Now , the measures of the sides of the rectangle be

The length of the rectangle = L

The width of the rectangle = W

And , Area of Rectangle = Length x Width

On simplifying , we get

Area of rectangle = LW

when the dimension of one of the unit is decreased , we get

when L = L/2

Area of rectangle = ( LW) / 2

So , the area of the figure is decreased bu ( 1/2 )

Hence , the area of the figure decreases

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Answer:

b

Step-by-step explanation:

Answer:

(x45)

Step-by-step explanation:

(x2) (x4) (x-5)

(x8) (x-5)

(x45)

The vertex form of the quadratic equation is:

[tex]h(x) = (x - 3)^2 - 6[/tex]

For a quadratic equation:

[tex]y = a*x^2 + b*x +c[/tex]

With vertex (h, k), the vertex form is:

[tex]y = a*(x - h)^2 + k[/tex]

In this case, we have the equation:

[tex]h(x) = x^2 - 6x + 3[/tex]

To get the x-value of the vertex we use the general formula:

[tex]h = -(-6)/(2*1) = 6/2 = 3[/tex]

To get the y-value, we evaluate the function in x = 3, so we get:

[tex]h(3) = k = (3)^2 - 6*3 + 3 = -6[/tex]

So the vertex is (3, -6).

Then the vertex form is:

[tex]h(x) = (x - 3)^2 - 6[/tex]

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Answer:

1/4

Step-by-step explanation:

there are 12 options, and only three are correct.  3/12 simplifies to 1/4

Answer:

1/4

Step-by-step explanation:

There are 12 possible outcomes

The ones that have a head and an even number are H2  H4   H6

P( head and even number) = head and even number/ total outcomes

                                             = 3/ 12

                                              =1/4

Answer:

C.210

Step-by-step explanation:

360 degrees in a circle. 360-150=210

Answer:

competitions

Step-by-step explanation:

I got it right.

Answer:

Step-by-step explanation:

Let the numbers be x and y

Sum = x + y

Sum = one number + 20

[tex]x + y = x + 20[/tex]

Cancel equal terms on both sides of the equation.

[tex]y = 20[/tex]

Again,

Finding another number

Sum = other number + 18

[tex]x + y = y + 18[/tex]

Cancel equal terms on both sides of the equation

[tex]x = 18[/tex]

Hence, The two numbers are 18 and 20.

Hope this helps..

Best regards!

Answer: 109.1 degrees

Step-by-step explanation:

To find the angle between the given vectors, we will use the formula below:

Cos(θ) = (U.V)/ |U|.|V|

Where

U = 13i - 8j

V = 2i + 9j

U.V = (2x13) + (-8×9)

U.V = 26 - 72

U.V = - 46

|U| = sqrt ( 13^2 + 8^2)

= sqrt ( 233) = 15.264

|V| = sqrt( 2^2 + 9^2)

= sqrt ( 85 ) = 9.22

Substitute all the value of the parameters into the formula

Cos ø = -46 / (15.3 × 9.2)

Cos ø = - 46 / 140.72

Cos Ø = - 32687

Find the cos inverse of the value

Ø = cos^-1( -32687)

Ø = 109.079 degrees

Therefore, the angle between the given vectors to the nearest tenth of a degree is 109.1 degrees

Answer:

Step-by-step explanation:

sec (-x)-sin (-x) tan (-x)=cos x

sec(x)-(-sin x)(-tan x)=cos x

1/cos x-sin x(sin x/cos x)=cos x

multiply by cos x

1-sin ²x=cos²x

or 1=sin²x+cos²x

which is true.

Answer:

See below

Step-by-step explanation:

To create a dot plot:

We need to draw/put dots with the given data.

You'll find your answer in the attached file.

Let me know if it's not clear!

Answer:

1410

Step by step explanation:

2/5x=564

5/2*2/5x=564*5/2

x=1410

Proof: 2/5*1410=564

Hope it helps <3

Answer:

1410

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

16 people =7

7*5= 16*5

35=80 people

Answer:

80 people are required to run 35 machines

Step-by-step explanation:

Write and solve an equation of ratios:

  p       35

------- = -----

 16         7

where p is the number of people needed to run 35 machines.

Cross-multiplying yields 7p = 16(35), or p = 16(5), or p = 80

80 people are required to run 35 machines.

Answer:

-3

Step-by-step explanation:

To find the average of different numbers, first you add them all up. So -5+-7+-2+2+-3+=-15. Then, you divide the sum of all the numbers by the amount of numbers there were. So in this case, there were 5 numbers so we would divide the sum of all of them by 5. So now we do -15/5=-3.

Another example of finding the average of numbers is 15+4+10+9+3+1. So first we add them up and we get 42, then again, we divide by the amount of numbers there are. So we do 40/6 and we get 7, so the average is 7.

I hope this helped.

Answer:

the radius of the pool is 50.025 feet

Step-by-step explanation:

From the information given:

We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.

So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:

[tex]r^2 + 49^2 = ( r + 20 )^2[/tex]

[tex]r^2 +2401 = r^2 + 40r + 400[/tex]

[tex]2401 = 40r + 400[/tex]

[tex]2401- 400 = 40r[/tex]

2001 = 40 r

r = 2001/40

r = 50.025 feet

Answer:

¢51

Step-by-step explanation:

The price of once ounce of hair conditioner is 2.55 divided by 5 which is equal to 0.51. Convert that into cents and you get: ¢51.

Answer:

10m

Step-by-step explanation:

We can set up an equation to solve this.

[tex]\frac{20}{25} =\frac{8}{x}[/tex]

This equation can be created since we are given two similar sides of both triangles.

Now, cross multiply and simplify to solve for [tex]x[/tex].

[tex]20x=200\\x=10[/tex]

The answer is sensible, and if you put 10 into the same equation from earlier, you will see that it is accurate.

Therefore, the value of [tex]x[/tex] is 10m.

Answer:

about 91.2 cm³

Step-by-step explanation:

Radius (r) = diameter / 2 = 4.4 / 2 = 2.2

Volume of cylinder = πr²h, we know π = 3.14, r = 2.2 and h = 6

V = 3.14 * 2.2² * 6 = 91.2

Answer:

91.2

Step-by-step explanation:

To find the volume you need to use the formula [tex]\pi r^2h[/tex]

When you substitute all of the numbers the answer will be 91.1856

Answer:

x=2, y=20

Step-by-step explanation:

20x+3y=20-20x+5y=60

Combine like terms, so you would do plus 20x both sides and minus 3y both sides.

After that you can also do minus 20 both sides.

So you are left with 40x=2y=40

Answer:

Step-by-step explanation:

Pythagorean Theorem: a^2+b^2=c^2.

15^2+ b^2=25^2

225+b^2= 625

b^2=400

b= 20 or x=20

Answer:

x = 20

Step-by-step explanation:

This is a right triangle and we know 2 of the points so we can use the Pythagorean Theorem to solve.  The formula for the Pythagoreom Theroem is a^2 + b^2 = c^2. Side a is 15 and Side b is x. Side c or the hypotenuse is 25. Let's solve for side b:

a^2 + b^2 = c^2

15^2 + b^2 = 25^2

225 + b^2 = 625

Subtract 225 from both sides to get b^2 alone.

b^2 = 625 - 225

b^2 = 400

Find the square root of both sides.

b = 20 or x =  20

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Answer:

One solution: When the graphs intersect at one point

No solution: This means that the lines are parallel or that there is no answer to the equation

Infinite solutions: This means that any value for the variable would make the equation true

Step-by-step explanation:

Answer:

XY = 24 units

Step-by-step explanation:

First of all, we need to some construction here.

Let us draw a line parallel to XY from point P towards OX, which cuts OX at point Q.

Please refer to the attached figure.

Now, Let us consider triangle OQP which is a right angled triangle, with

Hypotenuse, OP = 26 units

Height, OQ = OX - PY = 16  - 6 = 10 units

Base, PQ = ?

We can use pythagorean theorem here to find the value of PQ.

According to pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OP^{2} = PQ^{2} + OQ^{2}\\\Rightarrow 26^{2} = OQ^{2}+10^{2} \\\Rightarrow PQ^{2} = 26^{2}-10^{2} \\\Rightarrow PQ^{2} = 676-100 \\\Rightarrow PQ^{2} = 576\\\Rightarrow PQ= 24\ units[/tex]

Now, we can see that side PQ is equal to side XY.

[tex]\therefore[/tex] XY = 24 units is the answer.

Answer:

{y = 1/4x^2 − 2 y = −1/2x}

(0,0)

(-6,3)

Step-by-step explanation:

Rewrite as system of equations

y=-1/2x

1/4x^2-2y=-1/2x

Move expression to left and change its sign

y+1/2=0

1/4x^2-2y+1/2x=0

Multiply both sides of equation by 2

2y+x=0

1/4x^2-2y+1/2x=0

Sum the equation vertically and eliminate variable (2y)

3/2x+1/4x^2=0

Solve the equation

x=0

x=-6

Substitute the value of x into equation

y+1/2*0 = 0

y+1/2*(-6) = 0

Solve equation for y

y=0

y=3

so the solution is

(x1,y1)=(0,0)

(x2,y2)=(-6,3)

Answer:

(13,15)

Step-by-step explanation:

If the trapezoid were to be reflected over the line segment BC, the new coordinates of point A would be (13,15) as it moves to right 5 points from BC sides.

Answer:

(B) 13,15

Step-by-step explanation:

If we look at point A in relation to point B, we see that it's 5 units to the left and 3 units down from point B, therefore making it at (3,15). Now, if we reflect across line BC (which is a y-axis) then we change the X value, not the y value. If the line BC is located at X=8, then the X value will be 8+5, since point A is 5 units away from the line BC. The y value will stay the same because we are reflecting over only one axis. 8+5 = 13, and the y stays at 15, so the new point value of A would be (13,15).

Hope this helped!

Answer:

f = 27

Step-by-step explanation:

11 = f - 16

Add 16 to both sides.

11 + 16 = f - 16 + 16

27 = f

Answer:

(x−3)(x+8)

Step-by-step explanation:

The middle number is 5 and the last number is -24.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 5

Multiply together to get -24

Can you think of the two numbers?

Try -3 and 8:

-3+8 = 5

-3*8 = -24

Fill in the blanks in

(x+_)(x+_)

with -3 and 8 to get...

(x-3)(x+8)

Answer:C

Step-by-step explanation:It’s C on edge

Answer:

D. 25 inch²

Step-by-step explanation:

Area of sector of a circle =(r^2∅) /2

where,

r = radius of the circle

∅= angle subtended by the arc at the center of circle in radians.

Given :

∅ =155°  

radius =4.3 in

Convert 155° to radian

πradian=180°

155°=π / 180°*155°

=2.705 radians

Area of sector of a circle =(r^2∅) /2

=(4.3^2 * 2.705) / 2

=(18.49 * 2.705) / 2

=50.01545 / 2

=25.007725 inch²

Approximately 25 inch²

25in^2

hope this helpsss ✓✓✓