3. At the bank, Sheila made 6 deposits, each in the same amount. Her sister Sherri made 5 deposits, each in the same amount. Each of Sherri's deposits was $10 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time?
(a) Write an equation. Let x represent the amount of one of Sheila’s deposits.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.

Answer:

8

Step-by-step explanation:

I'm going to guess there's a typo in the question and it should be

In 16 years, Ben will be 3 times as old as he is right now.

x + 16 = 3x

subtract x from both sides

16 = 2x

Divide both sides by 2

8 = x

x = 8

Answer:

See below

Step-by-step explanation:

Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.

Let's do [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] as an example

By using the power rule where [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex], then [tex]f'(x)=12x^3+6x^2-10x[/tex]

Now set [tex]f'(x)=0[/tex] and solve for [tex]x[/tex]:

[tex]0=12x^3+6x^2-10x[/tex]

[tex]0=2x(6x^2+3x-5)[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}[/tex]

[tex]x=\frac{-3\pm\sqrt{9+120}}{12}[/tex]

[tex]x=\frac{-3\pm\sqrt{129}}{12}[/tex]

[tex]x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}[/tex]

[tex]x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}[/tex]

[tex]x_1=0,x_2\approx0.6965,x_3=-1.1965[/tex]

By plugging our critical points into [tex]f(x)[/tex], we can see that our extreme values are located at [tex](0,7)[/tex], [tex](0.6965,5.956)[/tex], and [tex](-1.1965,2.565)[/tex].

The second derivative would be [tex]f''(x)=36x^2+12x-10[/tex] and plugging in our critical points will tell us if they are minimums or maximums.

If [tex]f''(x)>0[/tex], it's a minimum, but if [tex]f''(x)<0[/tex], it's a maximum.

Since [tex]f''(0)=-10<0[/tex] then [tex](0,7)[/tex] is a local maximum

Since [tex]f''(0.6965)=15.822>0[/tex], then [tex](0.6965,5.956)[/tex] is a local minimum

Since [tex]f''(-1.1965)=27.18>0[/tex], then [tex](-1.1965,2.565)[/tex] is a global minimum

Therefore, the extreme values of [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] are a global minimum of [tex](-1.1965,2.565)[/tex], a local minimum of [tex](0.6965,5.956)[/tex], and a local maximum of [tex](0,7)[/tex].

Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.

Answer:

Not sure but I think it's B.

Andre rode 1 mile in 8 minutes. In 2 minutes he will ride 16 minutes, we know this because he is riding at a constant speed. Now, lets turn this into an equation. Due to the fact that the speed is consent at 8 minutes a mile, with d being the distance in miles, we can say that y = 8d

Lets test this equation out:

y = 8d  1 minute

y = 8

y = 8d 2 minutes

y = 16

I hope this helps! :)

Answer:

Tbh i don’t really know

Step-by-step explanation:

Ask someone else

[tex]f(a) = -4a +6a^3 - 15 -4a^2 \\\\\text{By the remainder theorem,}\\\\f\left(\dfrac 53 \right) = -4\left(\dfrac 53 \right) + 6 \left( \dfrac 53 \right)^3 - 15 - 4 \left(\dfrac 53 \right)^2 = -5\\\\\\ \text{Hence}~-5~ \text{is the remainder when f(a) is divided by}~ 3a -5[/tex]

[tex]\\ \sf\longmapsto 3a-5=0[/tex]

[tex]\\ \sf\longmapsto 3a=5[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{5}{3}[/tex]

Using remainder theorem

[tex]\\ \sf\longmapsto f(a)=-4a+6a^2-4a^2-15[/tex]

[tex]\\ \sf\longmapsto f\left(\dfrac{5}{3}\right)[/tex]

[tex]\\ \sf\longmapsto -4(5/3)+2a^2-15[/tex]

[tex]\\ \sf\longmapsto -20/3+2(5/3)^2-15[/tex]

[tex]\\ \sf\longmapsto -20/3+2(25/9)-15[/tex]

[tex]\\ \sf\longmapsto -20/3+50/9-15[/tex]

[tex]\\ \sf\longmapsto (-60+50)/9-15[/tex]

[tex]\\ \sf\longmapsto -10/9-15[/tex]

[tex]\\ \sf\longmapsto -10-135/9[/tex]

[tex]\\ \sf\longmapsto -145/9[/tex]

[tex]\\ \sf\longmapsto 16\dfrac{-5}{9}[/tex]

Remainder=-5

Step-by-step explanation:

Angles whose sum is 90° .

For ex - 30° and 60°

Answer/Step-by-step explanation:

Complementary angle is two angle that add up to 90 degree.

Complementary angle also put together form a right angle.

ex:

To determine the complement, subtract the given angle from 90. 90 - 43 = 47° The complement of 43° is 47°.

Answer:

[tex]2^{2} *3^{2}[/tex]

Step-by-step explanation:

You would have to prime factorize the number.

36=4x9

4=2x2

9=3x3

36=2x2x3x3

Answer:

36 reduced into simplest form is 12.

Step-by-step explanation:

12 is the simplest form of 36 because it has the smallest numerator and denominator possible to represent that amount.

Answer:

17 IS THE ANSWER......................

Answer:

Your answer should be 36.

Answer:

21

Step-by-step explanation:

Create an equation: 3n - n = 14

Solve: 3n - n = 14

          2n = 14

           n = 7

Larger number: 3(7) = 21

Answer:

The numbers are 7 and 21.

Step-by-step explanation:

The difference is 14 and 7*3= 21

Answer:

1,408

Step-by-step explanation:

208 + 363 + 837=1408

Answer:

25 little box will fit in the large box

Step-by-step explanation:

50×30×20=3000

10×3×4=120

so 3000/120=25

Answer: 25

Step-by-step explanation:

big cuboid=abc=50×30×20=3000cm3

little cuboid=10×3×4=120cm3

3000÷120=25

Answer:

t = 337.5

Step-by-step explanation:

(7.5) * 7.5t = 45 * (7.5)

t = 337.5

Just some simple algebra, please mark me brainliest!

Answer:

70.61 is a rational number

Step-by-step explanation:

This is because a rational number is either:

A whole number, like 70, whole number.

Is a terminating decimal, such as the one above 70.61, (A terminating decimal is a decimal that doesn't repeat.

And or has a pattern, or a recurring decimal, like 7.478478..., it repeats the decimal over and over, thus, rational.

Hope this helped you, have a great day.

Answer: Option 3 is the answer hope this helps!

Step-by-step explanation: Option 3

Answer:

length:   5x + 2

width:   x - 2

Step-by-step explanation:

Factors of 5

1, 5

Factors of 4

1, 4

2, 2

Sign

one positive, one negative

Factor 5x^2 - 8x - 4

(5x + 2)(x - 2) = 5x^2 - 10x + 2x - 4

(5x + 2)(x - 2) = 5x^2 - 8x - 4

Therefor

length:   5x + 2

width:   x - 2

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope (and always the factor of x). it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.

b is the y-intercept, the y value of the point, where the line crosses the y-axis (in other words : the y value when x = 0).

so, look at the chart. where do we see points with integer coordinates (these are the easiest to read correctly and work with) ?

I see for example (0, -6) and (4, -7).

to go from the first to the second point :

x changes by +4 units (from 0 to 4).

y changes by -1 unit (from -6 to -7).

the slope a is therefore -1/4.

and the first point i picked gives us also automatically the y-intercept (-6).

so, the line equation is

y = (-1/4)x - 6

Answer:

it's "2+6556_789*4236+8765/987"

Step-by-step explanation:

Answer:

neither, neither, terminating, repeating

Answer:

Step-by-step explanation:

x= fund that got 7%

y= fund that got 3%

x+y=3000

.07x+.03y=142

y=3000-x

.07x+.03(3000-x)=142

.07x+90-.03x=142

.04x=52

x= 1300

x+y=3000

1300+y=3000

y=1700

1300 in the fund that earned 7%

1700 in the fund that earned 3%

Answer:

13

Step-by-step explanation:

b2-12a

2(8)-12(1/4)

16-12/4

16-3

13

Answer:

32%

Step-by-step explanation:

Answer:

I have difficulty understanding the question.  I read it as "What is the value of  a number that when multiplied by 0.3 times (8/4) is equal to 34.55.  This doesn't seem correct, but if it is:

Step-by-step explanation:

(0.3)*(8/4)x = 34.55

(8/4)x = 115.17

x = (4/8)*(115.17)

x = 57.58

21 is the correct answer.

Answer:

Step-by-step explanation:

Answer:

16.4% quick maths, ya dig?

Answer:

Step-by-step explanation:

Remove The decimal,

= > 0.012 = 12/100

= > 3/25...ans

Answer:

_____

Step-by-step explanation:

Im pretty sure it would be 45 ____