Find the sine of R. A)12/13 B)13/12 C)5/12 D)5/13

Solve each of the quadratic equations 3x=0.5x2

aalyn [17]

Answer:

$3x = 1 \\ x = \frac{1}{3}$

6 0

3 years ago

Write the polynomial in factored form. p(x)=(x+5)(x-___)(x+___)

Rom4ik [11]

Answer:

Step-by-step explanation:

Given : $p(x)=x^{3} +6x^{2} -7x-60$

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, $\text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Since constant term = -60

Leading coefficient = 1

$\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}$

$\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}$

Thus the possible roots are $\pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60$

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is $x^{2} +x-12$

And remainder is 0 .

So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting

$x^{2} +x-12=0$

$x^{2} +4x-3x-12=0$

$x(x+4)-3(x+4)=0$

$(x-3)(x+4)=0$

Thus x-3 and x+4 are the other two factors

So , p(x)=(x+5)(x-3)(x+4)

3 0

4 years ago

Read 2 more answers

plz help !! write two real world situations that you can model using the exponential function f(x)=2 to the power of x

Margaret [11]

Answer:

Two real world situations are shown below.

Step-by-step explanation:

Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is

$f(x)=1(2)^x$

$f(x)=(2)^x$

A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is

$f(x)=1(2)^x$

$f(x)=(2)^x$

7 0

3 years ago

I tried to solve this problem and can’t can you tell me the answer

Kitty [74]

6/8 because maybe you could try the butterfly strategy and the answer would probably be 6/8

6 0

3 years ago

20 POINTS PLEASE HELP QUICKLY!!

SIZIF [17.4K]

Answer:

They will each have saved $70.

Jessica is saving at a faster rate than Raphael.

The rate at which Jessica is adding to her savings is $4 per week more than the rate at which Raphael is adding to his savings.

Step-by-step explanation:

The formula for Jessica’s savings is

y = 10x + 20

She is saving at the rate of $10/wk .

From Raphael’s table, he started with $40 and is saving at the rate of $6/wk.

The formula for Raphael’s savings is

y = 6x +40

When the two savings are equal

10x + 20 = 6x + 40 Subtract 20 from each side

10x = 6x + 20 Subtract 6x from each side

4x = 20 Divide each side by 4

x = 5

Their savings will be equal after five weeks.

=====

After five weeks , Jessica will have saved

y = 10×5 + 20

y = 50 + 20

y = $70

Raphael has also saved $70.

=====

Jessica is saving at a faster rate than Raphael.

She is saving at the rate of $10/wk, while he is saving at the rate of $6/wk.

The rate at which Jessica is adding to her savings is $4/wk more than the rate at which Raphael is adding to his savings.

The red line in the graph shows that Jessica starts with $20. After five weeks, she has caught up to Raphael, who also has $70 after five weeks.

6 0

3 years ago