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zhuklara [117]
3 years ago
5

Heather and Alyssa are saving money for summer break. Heather currently has $50 in her savings account and she will save $25 per

week until summer break. Alyssa currently has $200 in her savings account and she will save $10 per week. They want to know when they will have the same amount of money in their bank accounts. Which system of equations represents this situation?
Mathematics
2 answers:
atroni [7]3 years ago
7 0

Answer:

10 weeks, Substituion Equation.

Step-by-step explanation:

(Assume that x= 'per week').

We can write this as 50 + 25x=y for Heather's savings, &

                               200 + 10x=y for Alssa's savings.

We can combine these equations to make 200 +10x= 50+25x, because we know 50+25x=y, like we found out in the first equation. We can now subtract 25x from each side, and subtarct 200 from each side, to get

10x - 25x = 50 - 200, which can be simplified to -15x=-150. If we divided each side by -15, we get 10. Therefore, it will take 10 weeks for them to have the same amount of money. I think this is the Substituaion Equation

Setler79 [48]3 years ago
4 0

Answer:

Tilt your head back and allow your mouth to hang open widely.

Contract the back of the throat and breathe deeply through your mouth.

Inhale and exhale completely while relaxing the shoulders.

When the yawn comes “reach and extend into it” to stretch the jaw muscles.

Step-by-step explanation:

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The force F between 2 objects is inversely proportional to the square of the distance, d between them. The force is 0.36 newtons
LenaWriter [7]

Answer:

0.73 N to 2 dp.

Step-by-step explanation:

F = k/d^2   where k is a constant , F = force and d = distance.

Substituting:

0.36 = k / (6)^2

k = 36*0.36 = 12.96 s the equation is F = 12.96 / d^2.

When d = 4.2 :

F = 12.96 / 4.2^2

F = 0.73 Newtons to 2 dp.

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3 years ago
How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 3 years? The account pays 5.9
ra1l [238]

We are asked to determine the present value of an annuity that is paid at the end of each period. Therefore, we need to use the formula for present value ordinary, which is:

PV_{ord}=C(\frac{1-(1+i)^{-kn}}{\frac{i}{k}})

Where:

\begin{gathered} C=\text{ payments each period} \\ i=\text{ interest rate} \\ n=\text{ number of periods} \\ k=\text{ number of times the interest is compounded} \end{gathered}

Since the interest is compounded semi-annually this means that it is compounded 2 times a year, therefore, k = 2. Now we need to convert the interest rate into decimal form. To do that we will divide the interest rate by 100:

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Now we substitute the values:

PV_{ord}=4000(\frac{1-(1+0.059)^{-2(3)}}{\frac{0.059}{2}})

Now we solve the operations, we get:

PV_{\text{ord}}=39462.50

Therefore, the present value must be $39462.50

8 0
1 year ago
Fairfield Elementary has 14 sets of building blocks. There are 125 blocks in each set. How many blocks are there altogether?
yan [13]

Answer:

1,750 building blocks.

Step-by-step explanation:

In order to find the solution to this question, you must use multiplication.

If there are 14 sets of building blocks with 125 blocks each, in order to find the total amount of blocks we multiply 14 by 125.

You should get 1,750 as your final answer.

6 0
2 years ago
Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims
hjlf

Answer:

12 miles

Step-by-step explanation:

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 1/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

Total distance Alyssa cycled and ran =

\frac{4}{5} + \frac{1}{8}

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Mnenie [13.5K]

Answer:

Step-by-step explanation:

If two numbers have the same base, add the powers

5³ * 5⁴ = 5⁽³⁺⁴⁾ = 5⁷

6 0
3 years ago
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