Judy and Cassie each opened a savings account on the same day. Judy started by putting $300 in her account, and she will deposit an additional $12 each week. Cassie made an initial deposit of $100, and she will add $20 more each week. Eventually, Judy and Cassie will each have the same amount saved. How many weeks will that take?
Write a system of equations, graph them, and type the solution.

Using improper fractions, it is found that she carried 0.583 pounds more with her left hand than with her right hand.

The conversion is made according to the following formula:

[tex]a\frac{b}{c} = a + \frac{b}{c} = \frac{ac + b}{c}[/tex]

In her right-hand, the amount she carried is given by:

[tex]2\frac{1}{6} + 1\frac{2}{3} = \frac{13}{6} + \frac{5}{3} = \frac{13}{6} + \frac{10}{6} = \frac{23}{6}[/tex]

In her left-hand, the amount was of:

[tex]4\frac{5}[12} = \frac{53}{12}[/tex]

The difference is of:

[tex]\frac{53}{12} - \frac{23}{6} = \frac{53}{12} - \frac{46}{12} = \frac{7}{12} = 0.583[/tex]

She carried 0.583 pounds more with her left hand than with her right hand.

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Answer:

Solve for  x  in the first equation.

Subtract  8 y  from both sides of the equation.

2 x = 6 − 8 y

5 x + 20 y = 15

Divide each term by  2  and simplify.

Divide each term in  

2 x /2 =  6/2  − 8 y/2  

5 x + 20 y = 15

Cancel the common factor of  2 .

Cancel the common factor.

2 x /2  =  6 /2  + (− 8 y)/ 2

Step-by-step explanation:

I don't have room to put the rest. So go to math-way

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Answer:

[tex] A=(8 \pi +40) cm^2 [/tex]

[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]

Step-by-step explanation:

For semicircle:

Diameter = 8 cm

Radius (r) = 8/2 = 4 cm

For triangle:

Base (b) = 8 cm

Height (h) = 10 cm

Area of the shaded region

[tex] A=\frac {1}{2} \pi r^2 +\frac {1}{2}b.h[/tex]

[tex] A=\frac {1}{2} \pi (4)^2 +\frac {1}{2}(8).(10)[/tex]

[tex] A=(8 \pi +40) cm^2 [/tex]

By Pythagoras Theorem:

[tex] AC = BC = \sqrt {4^2 +10^2}[/tex]

[tex] AC = BC = \sqrt {16 +100}[/tex]

[tex] AC = BC = \sqrt {116}[/tex]

[tex] AC = BC =2\sqrt {29}[/tex]

[tex] P= \frac {1}{2} \times 2\pi r+ AC + BC[/tex]

[tex] P= \pi (4)+ 2\sqrt {29} + 2\sqrt {29}[/tex]

[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]

Two bikers are riding a circular path.

The first rider completes a round in 12

minutes. The second rider completes

a round in 18 minutes. If they both

started at the same place and time

and go in the same direction, after

how many minutes will they meet

again at the starting point?

[tex] \huge \mathsf \blue{Given}[/tex]

[tex] \huge \mathsf \blue{To\: Find}[/tex]

After how many minutes will they meet

again at the starting point?

Take the LCM of 12 and 18

12 = 2 × 2 × 3

18 = 2 × 3 × 3

Thus, the LCM of 12 and 18 is 36.

Answer:

Find the LCM of 12 & 18 .

12 = 2×2×3

18 = 3×3 ×2

So , LCM of ( 12 , 18 ) = 2×3×2 = 36

Answer:

h(x)=4x_2+2x+8

h(x)=6x+6

Answer:

Steps:

given:

f(x) = 4x-2

g(x) = 2x+8

h(x) = f(x) + g(x)

h(x) = 4x-2 + 2x+8

h(x) = 4x + 2x + 8 - 2

h(x) = 6x + 6

Answer:

25%

Step-by-step explanation:

Step 1: Add all the possible choices up

8 + 5 + 7 = 20

Step 2: Note that your finding the probability for creme filled ones

Step 3: Make it a fraction

5 creme filles ones out of 20

5/20

Step 4: Simplify

1/4

Step 5: Convert into a decimal (if you don't already know it)

1 ÷ 4 =

.25

Step 6: Multiply by 100 to find percentage

.25 × 100 = 25%

Answer:

x = 26.5

y = 12.0

z = 13.4

Step-by-step explanation:

✔️To find x, apply the leg rule, which is:

Hypotenuse/leg = leg/part

Hypotenuse = 30

Leg = x

Part = 30 - 6 = 24

Plug in the values into the equation

30/x = x/24

Cross multiply

x² = 30*24

x² = 720

x = √720

x = 26.5 (nearest tenth)

✔️Apply the triangle altitude theorem to find y:

Based on the theorem, h = √(ab)

Where,

a = 6

b = 30 - 6 = 24

h = y

Plug in the values

y = √(6*24)

y = √144

y = 12

✔️Apply the leg rule, Hypotenuse/leg = leg/part to find z:

Hypotenuse = 30

Leg = z

Part = 6

Plug in the values into the equation

30/z = z/6

Cross multiply

z² = 30*6

z² = 180

z = √180

z = 13.4 (nearest tenth)

Answer:

300....?

Step-by-step explanation:

Answer:

AD=11.7 since corresponding side of parallelogram are equal.

BD=8.5 since corresponding side of parallelogram are equal.

Answer:

#1

#2

Answer:

(7,4)

Step-by-step explanation:

The rule for reflecting over the x-axis is (x,y) -> (x,-y)

If you apply that to your point, you get (4,4)

When doing this translation, you add the 3 to the number you have in the x. This will give you (7,4).

Hope I helped.

Answer:

if these lines intersect the slopes must be different

Step-by-step explanation:

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept.

Answer:

Linear functions (or lines) have really only 2 attributes : The slope (indicating the inclination of the line), and the y-intercept (the intersection with the y-axis) or the x-intercept. Either way, they show the actual position of the line. The lines intersect at one point if they have different slopes. They intersect at infinitely many points, if the slope and the y or x-intercepts are equal (ultimately that means the lines are identical, so every point is an intersection point). If they have the same slope but different y or x-intercepts, it means they are parallel and will never intersect.

Answer:

3.5

Step-by-step explanation:

Answer: 3/5 or 0.6

Step-by-step explanation: It would take 2 shots for me to fine tune the force I need to get a perfect shot.  If you divide 3 by 5 you get 0.6.

Answer:

B

Step-by-step explanation:

add 7 to get away the 7 on the left hand side

square both side to eliminate square root

The first two steps in solving the radical equation are to Add 7 to both sides and then square both sides.

A radical is the opposite of the power, therefore, the roots are known as the radical. It is denoted as √, ∛, etc.

In order to solve the given radical, we will go through the following steps,

[tex]\sqrt{x+3}-7=15[/tex]

1.  Add 7 both the sides to eliminate -7 from both the sides,

   [tex]\sqrt{x+3}-7+7=15+7\\\\\sqrt{x+3}=22[/tex]

2. Square both the sides to remove the square root,

   [tex]\sqrt{x+3}=22\\\\(\sqrt{x+3})^2=22^2\\\\x+3 = 484[/tex]

Hence, the first two steps in solving the radical equation are to Add 7 to both sides and then square both sides.

Learn more about Radical:

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Answer:

170.67 cm^3

Step-by-step explanation:

The volume is given by ...

 V = 1/3s²h

We are given that 4s=32, so s=8. We are also given that h=8. (All linear dimensions are in centimeters.) Then the volume is ...

 V = (1/3)(8²)(8) = 512/3 = 170.67 . . . . cm³

Answer:

170.67 cm^3

Step-by-step explanation:

took the test

Answer:

36+50.27=86.27

86.27cm^2

Step-by-step explanation:

3.14x4^2= 50.27

9x8=72/2=36

add them up and boom there goes your gf ... jk jk jk

then u get the answer ofc ;)

Answer: Its B. Side a is 2 inches long and side b is 1.5 inches long.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The n-th term of arithmetic sequence:  [tex]a_n = a_1+d(n-1)[/tex]

a₁ = -30

a₂ = -41

a₃ = -52

-41 - (-30) = -11  and -52 - (-41) = -11

It means d = -11

Therefore:

              [tex]a_{65}=-30+(-11)(65-1)=-30-11\times64=-734[/tex]

Answer:

The first answer is 31.5.

The second is 21.

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

because 180- 140 = 40

a linear pair means they equal 180

The measure of angle ACD (∠ACD) is 40 degrees.

Given that angles ACD and DCB forms a linear pair, also m ∠DCB = 140°,

We are asked to find the measure of ∠ACD,

So,

If angles ACD and DCB form a linear pair, it means that their sum is equal to 180 degrees.

Let's denote the measure of angle ACD as x.

So, we have the equation:

m∠ACD + m∠DCB = 180°

Substituting the given value for m∠DCB:

x + 140° = 180°

To solve for x, we can subtract 140° from both sides of the equation:

x = 180° - 140°

x = 40°

Therefore, the measure of angle ACD (∠ACD) is 40 degrees.

Learn more about linear pair click;

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#SPJ2

Answer:

1,736km^2

Step-by-step explanation:

Answer:

2,352 km^2

Step-by-step explanation:

So there is a square and 4 triangles.

You first, find the area of the square.

You then get: 35 x 48 = 1,680

Then you need to add the triangles.

Because we have 2 triangles on each side the area formula of a triangle in which is 1/2 times by the base and height can be solved by just B * H.

Doing that you can get: 48 * 7 = 336

Because you have 2 triangles, the final area results in:

1,680 + 336 * 2 = 2,352

Answer:

x = 25°

Step-by-step explanation:

the angle adjacent to the 130 angle is 50 degrees

x = 180-(105+50)

x = 180-155

x = 25

Answer:

67 times

Step-by-step explanation:

Spinner's sample space = (1, 2, 3, 4, 5, 6)

Number less than 5 = (1, 2, 3, 4)

Total possible outcomes = 6

Required outcome = 4

P(number less than 5) = required outcome / Total possible outcomes

P(number less than 5) = 4 /6 = 2/3

Number of spins = 100

Predicted Number of times a number less than less than 5 is spurn in 100 spins :

100 * 2/3

= 66.666

= 67 times

Answer:

The first option

Step-by-step explanation:

Have a nice day :)