Sophia has $6,000 to invest. She is considering two investment options. Option A pays 2.2% simple interest. Option B pays 2% interest compounded annually. Use the drop-down menus below to choose which option is the best choice for Sophia for each number of years.

Given:

In the circle, [tex]m(\overarc{VUX})=152^\circ[/tex] and [tex]m(\angle MUV)=77^\circ[/tex].

To find:

The following measures:

(a) [tex]m\angle VUX[/tex]

(b) [tex]m\angle UXW[/tex]

Solution:

According to the central angle theorem, the central angle is always twice of the subtended angle intercepted on the same same arc.

[tex]m(VUX)=2\times m\angle VWX[/tex]

[tex]152^\circ=2\times m\angle VWX[/tex]

[tex]\dfrac{152^\circ}{2}=m\angle VWX[/tex]

[tex]76^\circ=m\angle VWX[/tex]

In a cyclic quadrilateral, the opposite angles are supplementary angles.

UVWX is a cyclic quadrilateral. So,

[tex]m\angle VUX+m\angle VWX=180^\circ[/tex]          [Opposite angles of a cyclic quadrilateral]

[tex]m\angle VUX+76^\circ=180^\circ[/tex]

[tex]m\angle VUX=180^\circ-76^\circ[/tex]

[tex]m\angle VUX=104^\circ[/tex]

Now,

[tex]m\angle UXW+m\angle UVW=180^\circ[/tex]          [Opposite angles of a cyclic quadrilateral]

[tex]m\angle UXW+77^\circ =180^\circ[/tex]

[tex]m\angle UXW=180^\circ-77^\circ[/tex]

[tex]m\angle UXW=103^\circ[/tex]

Therefore, [tex]m\angle VUX=104^\circ[/tex]  and [tex]m\angle UXW=103^\circ[/tex] .

Answer: x=-2

Step-by-step explanation:

Given

f(x)=2(3x+7)-4(x-2)

f(x)=18

Use substitution method

2(3x+7)-4(x-2)=18

Expand parenthesis

6x+14-4x+8=18

Combine like terms

2x+22=18

Subtract 22 on both sides

2x+22-22=18-22

2x=-4

Divide 2 on both sides

2x/2=-4/2

x=-2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

PE = 102.9 Joules

Step-by-step explanation:

PE = mgh

= (7.0 kg)(9.8 m/s^2)(1.5 m)

= 102.9 Joules

Answer:

The answer is C I know that is right

The square root of 49/900 is 7/30 according to the given question, it can be done through simplification process.

To find the square root of 49/900, we can simplify the fraction first:

The square root of a number is a mathematical operation that determines a value which, when multiplied by itself, yields the original number. In simpler terms, the square root of a number "x" is the value "y" such that y multiplied by y equals x. The square root is denoted by the radical symbol (√).

49/900 = [tex](7^2)/(30^2)[/tex]

Taking the square root of the numerator and denominator separately, we get:

√ [tex](7^2) /[/tex]√([tex]30^2[/tex])

Simplifying further, we have:

7/30

Therefore, the square root of 49/900 is 7/30.

To know more about  square root here

https://brainly.com/question/428672

#SPJ2

Let's solve your system by elimination.

8x+y=−16;3x−y=5

8x+y=−16

3x−y=5

Add these equations to eliminate y:

11x=−11

Then solve: 11x=−11 for x:

11x=−11

11x

11

=

−11

11

(Divide both sides by 11)

x=−1

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

8x+y=−16

Substitute: −1 for x in 8x+y=−16:

(8)(−1)+y=−16

y−8=−16(Simplify both sides of the equation)

y−8+8=−16+8(Add 8 to both sides)

y=−8

Answer:

x=−1 and y=−8

Answer:Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

Subtract the second equation from the first.

Solve this new equation for y.

Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To find the least number of leafs that each collection must have, we find the L.C.M of both numbers. So L.C.M of 4 and 5.

The prime factors of 4 = 2²

The prime factors of 5 = 5

So L.C.M of 4 and 5 = 2² × 5 = 20

So, the least number of leafs that each collection can have is 20 leafs.

Answer and Step-by-step explanation:

Work is in picture.

#teamtrees #PAW (Plant And Water)

Given:

The sequence is:

-15,-10,-4, 3, 11, ______

To find:

The next number.

Solution:

We have,

-15,-10,-4, 3, 11, ______

Here, the difference between two consecutive terms are:

[tex]-10-(-15)=-10+15[/tex]

[tex]-10-(-15)=5[/tex]

Similarly,

[tex]-4-(-10)=6[/tex]

[tex]3-(-4)=7[/tex]

[tex]11-3=8[/tex]

It is clear that the difference difference between two consecutive terms is increasing by 1. So, the next difference must be (8+1)=9.

Let the next number be x. Then,

[tex]x-11=9[/tex]

[tex]x=9+11[/tex]

[tex]x=20[/tex]

Therefore, the next number of the sequence is 20.

Answer:

C

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

Answer:

h its h :)

Step-by-step explanation:

i

Answer:

1= 1/6, 2= 1/6, 3= 4/6

Step-by-step explanation:

'1' and '2' are equal and only take up 1/6 of the "circle" each, leaving '3' with 4/6 of it.

Therefore, '1' and '2' would be placed 1/6 along the line, and '3' would be placed 4/6 along the line.

Answer:

Factor numerator and denominator

Step-by-step explanation:

Answer:

Kathryn thinks that the 3 is the age and the 10 is how many are that age. 10 is thr age and the 3 "x's" are how many people are 10 years old.

Hope this helped!

Answer:

B

Step-by-step explanation:

Answer:

78 is the range of high temperature

Answer:

8 students in each van, 22 students in each bus

Step-by-step explanation:

Let's say v is number of students in each van

and b the number of students in each bus.

Let's make the equations:

8v + 8b = 240

4v + 1b = 54

8v + 8b = 240

v + b = 30

b = 30 - v

now let's use b = 30 - v and insert it into 4v + 1b = 54

4v + (30 - v) = 54

3v + 30 = 54

3v = 24

v = 8

b = 30 - v = 30 - 8 = 22

Answer:

x9

Step-by-step explanation:

i dunno if correct

Answer:

6

Step-by-step explanation:

Since you're given g(-3), set up the equation to look like this:

g(-3) = (x+7) + 2

Then plug in the g(x):

g(x) = (-3 + 7) + 2

Use PEMDAS to solve the equation:

g(x) = (-3 + 7) + 2

g(x) = (4) + 2

g(x) = 6

Answer:

65

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sphere

1.V≈113.1m³

V=4 /3πr3=4/ 3·π·33≈113.09734m³

Sphere

2.R =6cm

Volume of sphere = 4/3πr^3

4/3πr^3=288π

r^3=288*3/4

r^3=216

r=6cm

Cone

3.V≈314.16m³

V=πr^2h/ 3=π·52·12/ 3≈314.15927m³

Cone

4. h≈2.55m

Using the formula

V=πr^2h/ 3

Solving for h

h=3V/ πr^2=3·96/ π·6^2≈2.54648m

Cylinder

5.V≈75.4m³

Solution

V=πr2h=π·22·6≈75.39822m³

Cylinder

6.h≈0.95m

Using the formula

V=πr2h

Solving for h

h=V/ πr^2=75/ π·5^2≈0.95493m

Hope this helped!!!

Answer:

6 -> 4/10

7 -> s √144 in

8 -> 0.4

9 -> s = ∛999 in

10 -> d = 3

Step-by-step explanation:

-5y=35

=35÷(-5)

= -7

=-5×-7

=35

Answer:

24 m²

Step-by-step explanation:

Given that:

Dimension of bedroom = 6 meter by 4 meter

To obtain how much carpet Lisa would need to cover the floor of her bedroom, we calculate the area of the room.

From the dimension given, the area of the room can be obtained using the Area if a rectangle formular :

Area of room = Length * width

Area of room = 6m * 4m

Area of room = 24 m²

Carpet required is 24m² of carpet

Answer:

24m

Step-by-step explanation:

if you times 6 and 4 that equals 24 really easy problem.

Answer:

I'm not sure what you mean by this question. Please clear it up.

Step-by-step explanation:

Answer:

they are possibly ip grabbers/will redirect you to some scam page don't click on them (obviously)

Step-by-step explanation: