Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it each month. Jodi's grandparents started Account B for her. It ccurently has $300 in it, and her grandparents deposit $40 into it each month.

Account A is modeled by the function f(x)=20x+100
and Account B is modeled by the function g(x)=40x+300
, where x
represent the number of months from now.

Write a new function (f+g)(x)
that represents the total amount of money Jodi has in both accounts. Simplify your answer.

Answer: 2760

Step-by-step explanation:

To find an equation of a line, you have to know the value of slope first. We can find the value of slope by using the formula below:

[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

m-term represents the slope from y = mx+b.

We are given two coordinate points. Substitute the points in the formula.

[tex] \large{m = \frac{7 - 5}{3 - 0} } \\ \large{m = \frac{2}{3} }[/tex]

Therefore the slope is 2/3.

Next we find the y-intercept. In the form of y = mx+b where m = slope and b = y-intercept. We have got slope, except the y-intercept. We can find the y-intercept by substituting one of gjven points in the equation of y = mx+b.

Since we know the slope - we can rewrite the equation like below:

[tex] \large{y = \frac{2}{3} x + b}[/tex]

Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.

[tex] \large{5 = \frac{2}{3} (0) + b} \\ \large{5 = 0 + b} \\ \large{b = 5}[/tex]

Thus the y-intercept is (0,5). Note that if the question gives you (0,a) point. That is the y-intercept of graph. So b = a if given (0,a).

Rewrite the equation by substituting the b-value.

[tex] \large{y = \frac{2}{3} x + 5}[/tex]

Hence, the equation of a line that contains those points is y = 2x/3 + 5

Answer

Hope this helps! Let me know if you have any doubts.

Answer:

(7/2, -9/2)

Step-by-step explanation:

to find the midpoint, we can use the midpoint formula, which is:

(x1+x2)/2, (y1+y1)/2

since we know the points (1,-1) and (6,-8) we can plug this into the formula:

for the x-coordinate: (1+6)/2=7/2 (or 3 1/2)

for the y-coordinate: (-1+(-8)/2=-9/2 (or -4 1/2)

so, the midpoint of the line segment would be (7/2, -9/2)

Answer:

(0.88, 0,65)

Step-by-step explanation:

what do we have to do ? I assume we need to find the crossing point between the 2 lines.

when looking at the graphic, we can already rule out the first, third and fourth option.

none of the coordinates of that point is larger than 1 in any direction or smaller than 0.5.

so, just by looking at things I immediately "bet" on answer option 2 (0.88, 0.65).

but let's check.

y = -2x/5 + 1

y = 3x - 2

for the crossing point both functions must produce the same functional value.

=>

-2x/5 + 1 = 3x - 2

-2x/5 + 5/5 = 15x/5 - 10/5

-2x + 5 = 15x - 10

15 = 17x

x = 15/17 = 0.88...

y = 3×0.88... -2 = 0.65...

hurray, our original observation and "suspicion" is confirmed.

Answer:

24

Step-by-step explanation:

Each book equals 1 so when you count all you will get 24

Answer:

k = 28

Step-by-step explanation:

[tex]t = 6n - 1 \\ 167 = 6k - 1 \\ 6k = 168 \\ k = 28[/tex]

Answer:

1) He measured an octagon

2) 89°

Step-by-step explanation:

All other conventional shapes are less than 900°. An octagon is 1080°. To find missing angle you [tex]1080-991=89[/tex]

Answer:

cubic polynomial

Step-by-step explanation:

3 is highest exponent and 3 is cubic

there are more than 3 terms, so it's polynomial (poly=many)

Answer:

find F

Step-by-step explanation:

this graph does not need to be in any order, but heres my suggestions to get it right:

Point B is ALWAYS on the opposite side of C

Answer:

your answer is D. 24 cubic cm

Step-by-step explanation:

your welcome good day :)

Answer:

replace the ys with -3 then solve it

Answer:

40

Step-by-step explanation:

4 + 3(4×3)

4+ 3(12)

4 + 36

= 40

hope this helps please like and mark as brainliest

Oh and please help me with my question

Answer:

11

Step-by-step explanation:

[tex] \frac{c + 49}{7} \\ = \frac{28 + 49}{7} \\ = \frac{77}{7} \\ = 11[/tex]

Answer:

[tex]x = \frac{7}{4} [/tex]

Step-by-step explanation:

[tex]−8(4x−10)=24[/tex]

[tex] \frac{ - 8(4x - 10)}{ - 8} = \frac{24}{ - 8} [/tex]

[tex]4x - 10 = \frac{24}{ - 8} [/tex]

[tex]4x−10=−3[/tex]

[tex]4x=−3+10[/tex]

[tex]4x=7[/tex]

[tex]x = \frac{7}{4} [/tex]

Answer:

[tex]x= \frac{7}{4} [/tex]

Step-by-step explanation:

Let's solve:

[tex]−8(4x−10)=24[/tex]

Step 1: Simplify both sides of the equation.

[tex]−8(4x−10)=24 \\ (−8)(4x)+(−8)(−10)=24(Distribute) \\−32x+80=24[/tex]

Step 2: Subtract 80 from both sides.

[tex]−32x+80−80=24−80 \\ −32x=−56[/tex]

Step 3: Divide both sides by -32.

[tex] \frac{ - 32x}{ - 32} = \frac{ - 56}{ - 32}

\\

x= \frac{7}{4} [/tex]

Answer: A.46

Step-by-step explanation: because it jus is dawg

Answer:

x - 6

Step-by-step explanation:

I am unfamiliar with such algebra tiles, but logically that set of tiles tells me :

1 x, -1, -1, -1, -1, -1, -1

so,

1×x + 6×(-1) = x - 6

Answer:

12.5

Step-by-step explanation:

We can use ratios to solve

4        4+6

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

5         AC

4        10

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

5         AC

Using cross products

4 * AC = 5*10

4AC = 50

Divide by 4

AC = 50/4

AC =12.5

Answer:

9 and 10

Step-by-step explanation:

square root of 86 is 9.2 (ish)

Answer:

x = 55 degree

Step-by-step explanation:

let the another angle be y

y+108=125 (sum of two interior opposite angle is equal to the exterioe angle formed)

y=125-108

y=17

y+x+108=180 degree (sum of interior angle of a triangle)

17 + x + 108 =180

x + 125 =180

x = 180-125

x=55

Answer:

first option

Step-by-step explanation:

[tex] {x}^{3} + 1 - (x - 1) \\ {x}^{3} + 1 - x + 1 \\ {x}^{3} - x + 2[/tex]

9514 1404 393

Answer:

  1.2 t/m³

Step-by-step explanation:

1 tonne is 1 Mg = 10⁶ g

1 m³ is (100 cm)³ = 10⁶ cm³

The conversion is ...

  (1.2 g/cm³) · (1 t)/(10⁶ g) · (10⁶ cm³)/(1 m³)

  = 1.2(10⁶)/(10⁶) t/m³

  = 1.2 t/m³

__

For this conversion, the numerical value does not change. Megagrams per cubic meter is the same ratio as grams per cubic centimeter.

Answer:

111

hope that helps!

Answer:

6 people

Step-by-step explanation:

8/40 = x/32

multiply both sides by 32: 8(32)/40 = x

x = 256/40

= 6.4

≈ 6

Answer:

1.27 centimeters

Step-by-step explanation:

brainliest??

Answer:

$30

Step-by-step explanation:

$120 per hour/4 hours=$30

Answer:

we don't see the graph, so we cannot tell anything.

Answer:

B

Step-by-step explanation:

Answer:

3 to 5

Step-by-step explanation:

There are 3 slices of pepperoni,  and there are 5 slices of cheese. Since it says pepperoni to cheese, peperoni would go first. Make sure to use order when calculating ratios.

Hope this helps! Have a wonderful rest of your day!

-kiniwih426

Answer:

--273

Step-by-step explanation:

100th term is equal a1 + 99d so

100th term = 222 + (-5×99) = -273

Answer:

35.00

Step-by-step explanation:

Sin(B)/b = Sin(A)/b

a* Sin(B) = b Sin(A)

b = a * Sin(B)/ Sin(A)

Plug in --> Get answer

The value of b is 34.75.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

From the law of sin,

Sin 29.8/c = Sin 34.5/22 = Sin B/b

Now,

The sum of the angles in a triangle is 180.

So,

∠A + ∠B + ∠C = 180

34.5 + ∠B + 29.8 = 180

∠B = 180 - (34.5 + 29.8)

∠B = 115.7

Now,

Sin 34.5/22 = Sin B/b

0.57/22 = Sin 115.7/b

0.57/22 = 0.90/b

b = (0.90 x 22) / 0.57

b = 34.74

Thus,

The value of b is 34.75.

Learn more about triangles here:

https://brainly.com/question/25950519

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