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3 years ago

What is the length and width of a rectangle given by the trinomial r squared - 6r- 55? Use factoring

Mathematics

1 answer:

alukav5142 [94]3 years ago

5 0

Answer:

The length and width are

r-11 and r+5

Step-by-step explanation:

The given trinomial is

${r}^{2} - 6r - 55$

To factor, we need to split the middle term to get:

${r}^{2} - 11r + 5r - 55$

We now factor by grouping to obtain;

${r}(r- 11) + 5(r - 11)$

We collect common factors again to get:

$(r- 11)(r + 5)$

Therefore the length and width are

r-11 and r+5

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A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 sen

Alik [6]

Answer:

Step-by-step explanation:

Firstly, we need to calculate the total score of the junior students and the total score of the senior students.

The total score of the junior students is 35 * 80 = 2,800

The total score of the senior students is 15 * 70 = 1050

The total score is thus 2,800 + 1,050 = 3,850

The average score of the 50 students is thus 3,850/50 which equals 77

8 0

3 years ago

Find two integers whose sum is -13 and product is 42

marta [7]

Answer:

they are -6 and -7

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

there were 18 cans ona shelf. a customer bought 7 cans. then jake put 6 cans on the shelf. how many cans are on the shelf now?

Rainbow [258]

18-7+6=17

17 cans are on the shelf.

3 0

3 years ago

Read 2 more answers

Please help me! Find the number x such that f(x) =1

STatiana [176]

Answer:

Step-by-step explanation:

We have the piecewise function:

$f(x) = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

And we want to find x such that f(x)=1.

So, let's substitute 1 for f(x):

$1 = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

This has two equations. So, we can separate them into two separate cases. Namely:

$1=-\frac{1}{2}x-1\text{ or } 1=x$

Let's solve for x in each case.

Case I:

We have:

$1=-\frac{1}{2}x-1$

Add 1 to both sides:

$2=-\frac{1}{2}x$

Let's cancel out the fraction by multiplying both sides by -2. So:

$2(-2)=(-2)\frac{-1}{2}x$

The right side cancels:

$-4=x\\$

Flip:

$x=-4$

So, x is -4.

Case II:

We have:

$1=x$

Flip:

$x=1$

This is the solution for our second case.

So, we have:

$x_1=-4\text{ or } x_2=1$

Now, can check to see if we have to to remove solution(s) that don't work.

Note that x=-4 is the solution to our first equation.

The first equation is defined only if x is less than -2.

-4 is less than -2. So, x=-4 is indeed a solution.

x=1 is the solution to our second equation.

The second equation is defined only if x is greater than or equal to -2.

1 is greater than or equal to -2. So, x=1 is also a solution.

Therefore, our two solutions are:

$x_1=-4\text{ or } x_2=1$

Out of our answer choices, we can pick D.

And we're done!

7 0

3 years ago

On a 15 hour trip, Rob drove 35% of the time and Mark drove the remainder of the time. How many hours did Mark drive? Explain 9.

Zigmanuir [339]

Answer:

9.75 hours

Step-by-step explanation:

If Rob drove 35% of the time and Mark drove the remainder of the time, the total is 100 %

100-35 = 65

so Mark drove 65% of the time

The total time driven was 15 hours, so we multiply the total time driven by the percentage of time that Mark drove to find the number of hours that Mark drove.

15 * 65%

15*.65

9.75 hours

7 0

3 years ago