PLEASE HELP ASAP !! UPVOTING What is the direct linear variation equation for the relationship?

Write a 2-column proof to prove the triangles congruent

Rom4ik [11]

Sure.

Statement Reason

-----------------------------------------------

AB=PL | Given

BC=LQ | Given

AC=PQ | Given

△ABC≅△PLQ | SSS

3 0

3 years ago

PLEASE HELP ILL GIVE BRANLIEST!!! ( and 50 points! )

Rama09 [41]

Answer:

As we know:

A nickle is worth 5 cents.

A dime is worth 10 cents.

A quarter is worth 25 cents.

Here is what Robert had:

Number of nickles (a)

Number of dimes (b)

Number of quarters (c)

Here is assumption:

5a + 10b + 25c = 850

a = 3b

c = b + 10

=> 5(3b) + 10b + 25(b + 10) = 850

=> 50b + 250 = 850

=> 50b = 600

=> b = 600/50 = 12

=> a = 3b = 3 x 12 = 36

=> c = b + 10 = 12 + 10 = 22

=> Number of nickles: 36

=> Number of dimes: 12

=> Number of quarters: 22

Hope this helps!

:)

8 0

3 years ago

What are the coordinates of the turning point of the graph of y=2x^2-4x+1?

kotykmax [81]

X=-b/2a=-(-4)/2(2)=4/4=1
y=2(1)^2-4(1)+1=-1
so the point is (1,-1)

8 0

3 years ago

Martin’s class is organizing a concert to raise money for a charity the graph below shows the relationship between the number of

frutty [35]

Answer:

$m=20n$

Step-by-step explanation:

Let

$A(5,100),B(10,200)$

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$slope=\frac{m2-m1}{n2-n1}$

substitute the values

$slope=\frac{200-100}{10-5}=20$

step 2

Find the equation of the line into slope-point

$m-m1=slope(n-n1)$

with the slope and the point A

$m-100=20(n-5)$

$m=20n-100+100$

$m=20n$

8 0

3 years ago

How Much Have I Saved? Portfolio

avanturin [10]

The time value of money calculation can be performed using formula equations or online calculators.

The correct responses are;

1) Option 3

2) Option 2

3) The difference in principal is approximately $8,000

The difference in interest earned is approximately $2,977.87

4) It is better to invest more money at the beginning of the 30 years

Reasons:

Option 1: Present value = 0

Amount invested per month, A = $25/month

The Annual Percentage Rate, APR, r = 3.25%

Number of years = 30

The future value of an annuity is given by the formula;

$\displaystyle FV_{A} = \mathbf{A \cdot \left (\frac{ \left(1 + \frac{r}{m} \right)^{m\cdot t} - 1}{\frac{r}{m} } \right)}$

In option 1, m = 12 periods per year

Therefore;

$\displaystyle FV_{A} = 25 \times \left (\frac{ \left(1 + \frac{0.0325}{12} \right)^{12 \times 30} - 1}{\frac{0.0325}{12} } \right) \approx \mathbf{15,209.3}$

Contribution = $25 × 12 × 30 = $9,000

Total interest earned = $15,209.3 - $9,000 = $6,209.3

Final balance = $15,209.3

Option 2: Present value = 0

Amount, A = $75/quarter

m = 4 periods per year

The Annual Percentage Rate, APR = 4.00%

Therefore;

The effective interest rate is therefore;

$\displaystyle r_{eff} = \left(1 + \frac{0.04}{4} \right)^4 - 1 \approx \mathbf{0.04060401}$

$\displaystyle FV_{A} = 75 \times \left (\frac{ \left(1 + \frac{0.04060401}{4} \right)^{4 \times 30} - 1}{\frac{0.04060401}{4} } \right) \approx 17,437.7$

Using an online calculator, FV = $17,467.04

Contribution = $75 × 4 × 30 = $9,000

Total interest earned = $17,467.04 - $9,000 = $8,467.04

Final balance = $17,467.04

Option 3: Present value = $1,000

APR = 6.25%

m = 12 period per year

Number of years, t = 30 years

Therefore;

$\displaystyle FV = \left (1 + \frac{0.0625}{12} \right)^{12 \times 30} \approx \mathbf{6,489.17}$

Contribution = $1,000

Total interest earned = $6,489.17 - $1,000 = $5,489.17

Final balance = $6,489.17

The table of values is therefore;

$\begin{tabular}{|c|c|c|c|}Option \# &Contribution &Total Interest Earned&Final Balance\\1&\$9,000&\$6,209.3 & \$15,209.3\\2&\$9,000&\$8,467.04 &\$17,467.04\\3&\$1,000&\$5,489.17&\$6,489.17\end{array}\right]$

1) The option that has the least amount invested are option 3

Option 3 investment plan is a present value of $1,000, invested for 30 years at 6.25% APR compounded monthly.

2) Option 2 yielded the highest amount at the end of 30 years, given that the APR is higher than the APR for option 1, although the amount invested over the period are the same.

The basis of option 2 investment plan is $75 invested quarterly at 4.00% APR compounded monthly for 30 years.

3) The difference in the principal invested for the highest and lowest final balance is $9,000 - $1,000 = $8,000

The difference in the interest earned is; $8,467.04 - $5,489.17 = $2,977.87

4) In option 1 the present value is zero, therefore zero amount was invested at the beginning.

The interest to investment ration is 6,209.3:9,000 ≈ 0.7:1

In option 3, all the money was invested at the beginning.

The interest to investment ratio of option 3 is; 5,489.17:1,000 ≈ 5.5:1

Given that the interest to investment ratio, which is the return on investment is larger when more money is saved at the beginning as in option 3, it is better to invest more money at the beginning.

Learn more about future value of an annuity here:

brainly.com/question/8243704

3 0

3 years ago