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2 years ago

EASY POINTS!!

Mathematics

2 answers:

irinina [24]2 years ago

6 0

Answer:

B. 64 square inches

Step-by-step explanation:

you just add

Elza [17]2 years ago

6 0

Answer:

Step-by-step explanation:

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Solve <img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D

Nostrana [21]

Answer:

$\displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}$

Step-by-step explanation:

we would like to solve the following equation for x:

$\displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x}$

to do so isolate $\frac{1}{x}$ to right hand side and change its sign which yields:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x}$

simplify Substraction:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)}$

get rid of only x:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)}$

simplify addition of the left hand side:

$\displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)}$

divide both sides by q+p Which yields:

$\displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)}$

cross multiplication:

$\displaystyle x(p + q + x) = - pq$

distribute:

$\displaystyle xp + xq + {x}^{2} = - pq$

isolate -pq to the left hand side and change its sign:

$\displaystyle xp + xq + {x}^{2} + pq = 0$

rearrange it to standard form:

$\displaystyle {x}^{2} + xp + xq + pq = 0$

now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so

factor out x:

$\displaystyle x( {x}^{} + p ) + xq + pq = 0$

factor out q:

$\displaystyle x( {x}^{} + p ) +q (x + p)= 0$

group:

$\displaystyle ( {x}^{} + p ) (x + q)= 0$

by Zero product property we obtain:

$\displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}$

cancel out p from the first equation and q from the second equation which yields:

$\displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}$

and we are done!

3 0

2 years ago

15 points please help

podryga [215]

Answer:

The range is y> 9

Step-by-step explanation:

8 0

3 years ago

Natalie is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 6 inches x 13 1/2 in

Leya [2.2K]

Answer:

1. 81

2. 108 1/2

3. 189 1/2

Step-by-step explanation:

7 0

3 years ago

Benjamín made 3 times more than Alberto and Carlota 2 times more than Benjamín, so how much is it, help me

vichka [17]

Step-by-step explanation:

you are "hiding" some more information (like how much they made together).

without that we cannot calculate the actual values.

all I can do is set up the equations expressing the given relations between the parts of the total :

a = amount Alberto made

b = amount Benjamin made

c = amount Carlota made

b = 3×a

c = 2×b = 2× 3×a = 6×a

that's it.

your see ? now we need something that "ties" all 3 together, an equation of all 3 variables, where we can use the first 2 equations (by substitution) and then solve for the remaining third variable.

and that is missing.

if it is something like "together they made x", then we would have

a + b + c = x

a + 3a + 6a = x

10a = x

a = x/10

b and c we get then from the first 2 equations by simply using the calculated value of a :

b = 3×(x/10) = 3x/10

c = 6×(x/10) = 6x/10 = 3x/5

7 0

2 years ago

Evaluate the given expression.

AleksAgata [21]

I believe the answer is B

3 0

2 years ago