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3 years ago

Write a system of equations to model each situation. Solve using any method:

Mathematics

1 answer:

ivolga24 [154]3 years ago

6 0

Answer:

a=50 b=20

Step-by-step explanation:

Call A and B the 2 present ages.

Ten years from now, A is twice as old as B -->

(A + 10) = 2(B + 10) (1)

Five years ago, A was 3 times as old as B -->

(A - 5) = 3(B - 5) (2).

Solve the system (1) and (2).

From (2) --> A = 3B - 15 + 5 = 3B - 10.

Replace this value of A into (1) -->

3B - 10 + 10 = 2B + 20 --> B = 20. Then,

A = 3B - 10 = 60 - 10 = 50.

Check

!0 years from now --> A = 60 and B = 30 --> A = 2B .OK

5 years ago --> A = 45 and B = 15 --> A = 3B. OK

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Juan is going to a school where tuition is $5,000 per year. He has a scholarship that pays 60% of his tuition. He has a grant fo

baherus [9]

Answer:

She now needs to borrow $4000

Step-by-step explanation:

Juan is going to a school where tuition is $5,000 per year. He has a scholarship that pays 60% of his tuition. He has a grant for $1,000 per year. How much will Juan need to borrow to pay tuition each year?

8 0

3 years ago

Please help! Will mark brainlessest

suter [353]

D.) D’(-3,-16)
Trans station is (x-5,y-16)

5 0

3 years ago

The diagram below shows an Isosceles triangle. Label the base angles and the vertex

Dmitry [639]

The base angles of an isosceles triangle are equal

The base angles are 15 degrees, while the vertex angle is 150 degrees

The base angles are given as:

Base = (6a- 3) and (a + 12)

So, we have:

$\mathbf{6a -3 =a + 12}$

Collect like terms

$\mathbf{6a -a =3 + 12}$

$\mathbf{5a = 15}$

Divide both sides by 5

$\mathbf{a = 3}$

Substitute 3 for a in Base = (6a- 3),

$\mathbf{Base = 6 \times 3 - 3}$

$\mathbf{Base = 18 - 3}\\$

$\mathbf{Base = 15}$

So, the base angle is 15 degrees.

The vertex angle is calculated using:

$\mathbf{Vertex=180 -2 \times Base}$

So, we have:

$\mathbf{Vertex=180 -2 \times 15}$

$\mathbf{Vertex=150 }$

Hence, the vertex angle is 150 degrees

Read more about isosceles triangles at:

brainly.com/question/25739654

6 0

2 years ago

3. Tamu has 17 cards. Richard gives her t cards. Tamu now has at least 38 cards. Which best describes Tamu’s cards? *

Shkiper50 [21]

I believe the answer is B

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3 years ago

Sum of all natural numbers from100to300 which are divisible by 4and 5 is

My name is Ann [436]

If $x$ is a number that is both divisible by 4 and 5, then

$\begin{cases}x\equiv0\pmod4\\x\equiv0\pmod5\end{cases}$

4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that $x=20n$ is a solution to the system, where $n$ is any integer. Simply put, any multiple of 20 fits the bill.

Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have $20n=100$ when $n=5$ , so the sum we want to compute is

$\displaystyle\sum_{n=5}^{15}20n=\boxed{2200}$

4 0

3 years ago