How many solutions are there to the following system of equations? 10x+5y=5 4x+2y=2

Pens come in packages of 6. Pencils come in

serious [3.7K]

A. The Least common multiple between 6 and 8 is 24, so you have to buy 4 packages of pens and 3 packages of pencils.

2. Since you bought 24 pens and 24 pencils, you have 48 pens and pencils in all

8 0

2 years ago

Read 2 more answers

What is b in terms of a and c?

aev [14]

Answer:

$b=\sqrt{c^2-a^2}$

Step-by-step explanation:

The given relation is

$c=\sqrt{a^2+b^2}$

To make $b$ the subject, we square both sides of the equation to get;

$c^2=(\sqrt{a^2+b^2})^2$

$c^2=a^2+b^2$

Isolate $b$ on one side of the equation;

$c^2-a^2=b^2$

Or

$b^2=c^2-a^2$

We take the positive square root of both sides to get;

$b=\sqrt{c^2-a^2}$

6 0

3 years ago

The institute of medicine determined that a man should drink 3 liters of fluids and a woman should drink 2.2 liters. Mr.Morrison

sergeinik [125]

They need to drink 3620 ml combined to meet the recommended amounts for the day.

5 0

2 years ago

Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is

Sladkaya [172]

Answer:

Option A.

Step-by-step explanation:

In an experiment a mouse took the mean time to find its way through a maze = 18 seconds.

So the mean time μ = 18

So null hypothesis says,

H₀ : μ = 18

Then a researcher thought that the mice can complete the maze faster than the time taken earlier.

So he thinks mean time taken by 10 mice will be less than 18 seconds.

Or μ < 18

Alternate hypothesis says will be

Hₐ : μ < 18

Therefore, null hypothesis and alternate hypothesis will be

H₀ : μ = 18

Hₐ : μ < 18

Option A. will be the answer.

4 0

2 years ago

In the diagram below, GH is parallel to DE . If GH is 3 more than EH FH=10, and DE=12 find the length of EH. Figures are not nec

steposvetlana [31]

Answer: 5

Step-by-step explanation:

Since $\overline{GH} \parallel \overline{DE}$ , by the corresponding angles theorem, $\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED$ . This means $\triangle FGH \sim \triangle FDE$ by AA.

As corresponding sides of similar triangles are proportional,

$\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5$
However, as distance must be positive, we consider the positive solution, x=5.

Therefore, the answer is 5

6 0

2 years ago