Ray has $30 saved and saves $2 a week and Joe has $90 saved and spends $4 a week when will they have the same amount of money saved?

Answer:Adding 5% interest to an account yearly has the same effect as taking 105% of its current value every year (you're taking all of your money - 100% of it - and adding an extra 5%, getting you 100% + 5% = 105%). This means that, if we started with $1000, after the first year, we'd have

1000(1.05) = $1050

after the second, and third years

1000(1.05)(1.05) = 1000(1.05)² = $1102.50

1000(1.05)(1.05)(1.05) = 1000(1.05)³ ≈ $1157.62

We can see a pattern starting to emerge. The 1000 always stays the same since its our starting value, but the power of the 1.05 goes up by 1 every year. In general, if we call the current value of the account in dollars y and the number of years it's been in the account x, then we can write this pattern generally as

Step-by-step explanation:

For a transition up you would add the number of h it’s of the transition to the y value and keep the x value the same

the transition would be (6, -5 + 1) = (6,-4)

draw the point at (6,-4) which would be one line above where the dot is now.

Answer:

The initial value of all linear functions that show a proportional relationship is 0. If it is a proportional linear relationship the origin of the function is at (0,0).

Answer:

keeping in mind that 21 months is more than a year, since there are 12 months in a year,  then 21 months is really 21/12 years.

Step-by-step explanation:

(picture)

so, clearly, you can see who's greater.

Answer:

120 grams

if they are all the same size

Answer:

[tex]1 \times 8 \times x = \frac{9}{8} \\ 8x = \frac{9}{8} \\ x = \frac{9}{64} [/tex]

Answer:

see attached

Step-by-step explanation:

See attached for step-by-step of the first problem.

The remaining two are solved in exactly the same way - just swap out the letters.

I've also attached the different exponent rules I've used.

Answer:

Step-by-step explanation:

[tex]12^{2x-1}=(\sqrt[4]{12})^{x}\\\\ 12^{2x-1}= (12^{\frac{1}{4}})^{x}\\\\12^{2x-1}=12^{\frac{1}{4}*x}\\[/tex]

Bases are same. So, compare the exponents.

[tex]2x - 1 =\dfrac{1}{4}x[/tex]

Multiply the entire equation by 4

4*(2x - 1) = x

8x - 4 = x

8x     = x + 4

8x -x  = 4

        7x = 4

         x = 4/7

Answer:

B) 3.14(144)

D) 2(3.14)(12)

E) 3.14(24)

Step-by-step explanation:

The formula to find the area of a circle is [tex]\pi r^2[/tex], where r = radius, while the formula to find the circumference of a circle is [tex]2\pi r[/tex] or [tex]\pi d[/tex], where r = radius and d = diameter.

Given the information above, option B) is a correct statement because 12^2 equals 144, and once you're done solving the square, you multiply it by 3.14. Next, option D) and E) are correct, too, because they exactly follow [tex]2\pi r[/tex] and [tex]\pi d[/tex]. Furthermore, for E), diameter = twice the radius, so it makes sense to multiply 3.14 by 24.

Answer:

The basketball that is 2 feet off the ground

Step-by-step explanation:

It is the closest to the floor and therefore has the least gravitational potential energy.

Only 1, 54.

There are obviously no such 1-digit numbers (1 - 9).

Let n = ab be a 2-digit number whose value is 6 times its digit sum, meaning

n = 10a + b = 6 (a + b)

Then

10a + b = 6a + 6b

4a = 5b

Now, 4 and 5 are coprime, so for equality to hold, a must be a multiple of 5 and b must be a multiple of 4.

The only valid multiple of 5 is 5 itself:

• a = 5   ⇒   5b = 20   ⇒   b = 4

There are 2 multiples of 4 to check. The first one gives the same result as a = 5.

• b = 8   ⇒   4a = 40   ⇒   a = 10

but a must be 1-digit.

So among the 2-digit numbers, only 1 such number exists, n = 54.

Let n = abc be a 3-digit number satisfying the criterion. Then

n = 100a + 10b + c = 6(a + b + c)

100a + 10b + c = 6a + 6b + 6c

94a + 4b = 5c

c must be a number from 1-9, which means at most 5c = 5•9 = 45.

If we take the smallest possible values of a and b, we have

94•1 + 4•0 = 94

but the smallest value of 94a + 4b is larger than the largest value of 5c.

So there are no such 3-digit numbers.

Answer:

Devon earned $86.45

Step-by-step explanation:

first, we know that the final price is 960.51 and we know that devon only gets 9% of that.

so we just need to multiply the final price by the percentage

960.51 x 9% = 86.445

then we round up to 86.45

Answer:

Devon earned $86.45

Step-by-step explanation:

first, we know that the final price is 960.51 and we know that devon only gets 9% of that.

so we just need to multiply the final price by the percentage

960.51 x 9% = 86.445

then we round up to 86.45

Step-by-step explanation:

The two lines intersect at one point so the system has exact same solution (one solution )

Angle beside 60°

Now

Sum of interior angles=exterior angle

Answer is False Solution

Step-by-step Explanation -

As per question,

[tex](5 + 1)^2- (12 + 3^2)= 3[/tex]

Now solving,

[tex]↪( {6}^{2} ) + (12 + 9) = 3[/tex]

[tex]↪36 + 21 = 3[/tex]

[tex]↪57≠3[/tex]

[tex]↪False \: Solution[/tex]

Therefore, Answer is not as per given options.

Therefore, it is a FALSE SOLUTION

Answer:

Step-by-step explanation:

let x,y be the sides of court.

2(x+y)=90

x+y=90/2=45

y=45-x

xy=500

x(45-x)=500

45x-x²=500

x²-45x+500=0

x²-25x-20x+500=0

x(x-25)-20(x-25)=0

(x-25)(x-20)=0

x=25,20

when x=25

y=45-x=45-25=20

when x=20

y=45-20=25

sides are 25 ft,20 ft.

Answer:

20 by 25 feet

Step-by-step explanation:

A = L·w

P = 2L + 2w

500 = Lw

90 = 2L + 2w

we could solve the first equation for 'w' and then substitute that value into the second equation:

w = 500/L

90 = 2L + 2(500/L)

90 = 2L + 1000/L

90 = (2L² + 1000)/L

multiply each side by L to eliminate it as the denominator

90L = 2L² + 1000

2L² - 90L + 1000

the zeros of this quadratic are 20 and 25

A = 20 x 25 which equals 500

P = 2(20) + 2(25) which equals 90

Answer:

28cm

Step-by-step explanation:

To calculate the area of this shape, we need to seperate it into two shapes.

We see that the length of the top shape is 2 CM.  Since the top shape is a square, we know it is a 2x2 shape (because two of the other sides are 2cm.)  The area of the top shape, the square, can be found by performing the formula for calculating area (length x width).  2 x 2 = 4 (duh, haha).  Now, we need to find the area of the bottom shape.  Since we're separating them into two shapes, we need to subtract the length of the first shape and this one.  4 x 6 (the area formula) will give us 24.  Now, we need to add our two shapes to get the area of the entire shape.  24 cm + 4 cm = 28 cm.

The answer is 21e + 35

Because there is not any value given

or

there should be like this:

21e + 35 = 161

21e = 161 - 35

e = 126 / 21

e = 6

If there is not like above example then the answer is 21e + 35

Step-by-step explanation:

option F HI = EF

hope this helps you!

Answer:

F

Step-by-step explanation:

with HI = EF we have then the SAS criteria fulfilled (side-angle-side, with the angle enclosed by the 2 verified sides).

Answer:

The hypotenuse would be 87.2

Step-by-step explanation:

We start by plugging in 13 for x for both sides of the triangle.

[tex]5(13)+5 = 70[/tex] and [tex]4(13) = 52[/tex].

Next, we use the Pythagorean theorem

[tex]a^2+b^2=c^2[/tex]

We plug in 70 for a and 52 for b

After plugging them in, you get [tex]4900+2704=c^2[/tex]

Now, we add a and b

[tex]7604=c^2[/tex]

Finally, take the sqrt of 7604

c = 87.2009174264, rounded to the nearest tenth is 87.2

Answer:

Hypotenuse = 87.2

Step-by-step explanation:

First find the lengths of the legs given the value of x

Left leg : 5x + 5

x = 13

5(13)+5

65 + 5 = 70

Bottom Leg : 4x

x = 13

4(13) = 52

So we have legs with lengths of 70 and 52 and knowing this we want to find the length of the hypotenuse.

We can do this by using the Pythagorean Theorem : a² + b² = c²

Where a and b = legs and c = hypotenuse

We are given the legs and we want to find the hypotenuse (c)

We can do this by plugging in the values of the legs into the Pythagorean Theorem and solving for c

Pythagorean Theorem : a² + b² = c²

a = 52 and b = 70

52² + 70² = c²

52² = 2704 and 70² = 4900

2704 + 4900 = c²

7604 = c²

take the square root of both sides

√7604 = 87.2 ( rounded to the nearest tenth ) and √c² = c

We're left with c = 87.2

The length of the hypotenuse is 87.2

Answer:

Solution,

hypotenuse (h)=x

perpendicular(p)=9

base(b)=53°

Using pythagoras theorem,

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {x}^{2} = {9}^{2} + {53}^{2} [/tex]

[tex] {x}^{2} = 81 + 2809[/tex]

[tex] {x}^{2} = 2890[/tex]

[tex]x = \sqrt{2890} [/tex]

[tex]x = 53.75[/tex]

hope it helps you

Answer:

10

Step-by-step explanation:

If b = 2, then b*5 = 10

Answer:

I think that is 45 b/c I am learning now that f(×)=6 like this c=15×3, c=45

Answer:

The area covered by a velocity-time(v-t) graph represents the distance covered by the body.

Simply find the area covered by graph.

If it's not easy to do so, then make different slots to find area, and at last add all of the slots' areas.

I hope it helped you! ;w;

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

if x-12=15

we add 12 to both sides

x-12+12=15+12

x=15+12

x=27.

To solve the problem we must know about the correlation coefficients.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

The correlation coefficient -0.9847 denotes, "There is a strong negative relationship between x and y".

Given to us

As we can see that the value of the correlation coefficient is 0.9847, therefore, it is close to 1 means the relationship is strong, while the '-' symbol denotes that the relationship is negative.

Hence, the correlation coefficient -0.9847 denotes, "There is a strong negative relationship between x and y".

Learn more about Correlation Coefficients:

https://brainly.com/question/15353989