Factor the following plynomial comletely -9x^2-30x-25

A biology test is worth 100 points and has 36 questions.

Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

$M + E= 36$ --- Number of questions

$2M + 6E = 100$ --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in $M + E= 36$

$E = 36 - M$

Substitute 36 - M for E in $2M + 6E = 100$

$2M + 6(36 - M) = 100$

$2M + 216 - 6M = 100$

Collect Like Terms

$2M - 6M = 100 - 216$

$-4M = - 116$

Divide both sides by -4

$M = \frac{-116}{-4}$

$M = 29$

Substitute 29 for M in $E = 36 - M$

$E = 36 - 29$

$E = 7$

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

$2M + 6E = 100$ would be:

$4M + xE = 100$

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

$4 * 29 + x * 7 = 100$

$116 + 7x = 100$

Subtract 116 from both sides

$116-116 + 7x = 100 -116$

$7x = 100-116$

$7x = -16$

Make x the subject

$x = -\frac{16}{7}$

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

6 0

3 years ago

Please help me asap will appreciate it a lot

attashe74 [19]

Answer:

1

Step-by-step explanation:

So for this type of problem we use the formula $m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ with each variable (besides m which is slope) representing a different coordinate. (e.g. -3 could be $y_{2}$ in this case.) First, let's define which is which:

(3,2): $x_{1}, y_{1}$

(-2,-3): $x_{2}, y_{2}$

Now we need to replace the variables with their known values: $m=\frac{-3-2}{-2-3}$

Next, let's do the subtraction to simplify: $m=\frac{-5}{-5}$

And we can complete the division (all fractions are division!) to simplify even further: $m = 1$

Therefore, the slope of the line passing through the points (3,2) and (-2,-3) is 1.

6 0

3 years ago

A fitness center currently has 320 members. Monthly memberships fees are $45. The manager of the fitness center has determined t

erma4kov [3.2K]

Answer:

The required equation :

$y=(320-10x)(45+5x)=14400+1150x-50x^2$

Step-by-step explanation:

Given : A fitness center currently has 320 members. Monthly memberships fees are $45. The manager of the fitness center has determined that each time the membership increases by $5, approximately 10 members leave and go to a different gym.

To write : A equation that can be used to find the revenue of the fitness center in dollars,y, after x price increases of $5.

Solution :

Revenue is defined by the amount or price during specific period.

Let x be the number of months,

y be the revenue of the fitness center.

The number of members in the fitness center is 320 but after increasing $5 10 members leave.

So, the total member after increment in x months are $320-10x$