A bookstore had 160 copies of magazines. yesterday it sold 3/8 of them. how many copies were sold yesterday?

Answers

Answer 1

Answer: If the bookstore has 160 copies, and they are dividing them into eights, then you need to divide 160 by 8. This will give you 20. That means that there are 20 copies of the magazine in each eighth. But they sold 3/8 of the magazines, not 1/8. So 20 x 3 equals 60. 3/8 of 160 is 60. The store sold 60 magazines yesterday.

Answer 2

Answer: This problem can be solved by simply multiplying 160 by 3/8.
$(3)/(8)$ x 160
$(3)/(8)$ x $(160)/(1)$
$(480)/(8)$
$60$
The bookstore sold 60 magazines yesterday.

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According to the Rational Roots Theorem, which statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 is true?Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.

Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Answers

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25.

Step-by-step explanation:

The Rational Root Theorems states that :

If the polynomial $P(x)= a _nx^n +{a_(n-1)x}^(n-1)+............{a_(2)x}^(2)+{a_(1)x}^(1)+a_0$ has any rational roots, then they must be in the form of

$\pm (factors of a_0)/(factors of a_n)$

Consider the polynomial

$f(x)=25x^7-x^6-5x^4+x-49$

in this case, we have $a_0=-49$ and $a_n=25$

Any Rational root of f(x) is a factor of $a_0=-49$ divided by a factor of $a_n=25$

According to the Rational Roots Theorem, the statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 which is true is:

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

The key points are "factors", and "ratio between the constant term and the coefficient of the highest order (exponent) term"

Question 1. In the below system, solve for y in the first equation. x + 3y = 6
2x − y = 10

one thirdx + 2
negative one thirdx + 6
−x + 2
negative one thirdx + 2

Question 2. What is the value of y in the solution to the following system of equations?

5x − 3y = −3
2x − 6y = −6

−1
0
1
2

Question 3. Solve 7x − 2y = −3
14x + y = 14

(4, five sevenths)
(4, seven fifths)
(five sevenths, 4)
(seven fifths, 4)

Question 4. Solve x + 3y = 9
3x − 3y = −13

(−1, ten thirds)
(1, negative ten thirds)
(−1, 3 over 10)
(1, negative 3 over 10)

Question 5. Use the substitution method to solve the following system of equations:

4x − y = 3
7x − 9y = −2

(1, 1)
(6, −3)
(6, 1)
(1, −3)

Question 6. Solve 5x − 6y = −38
3x + 4y = 0

(4, 3)
(−4, 3)
(4, −3)
(−4, −3)

Question 7. Solve 2x + 5y = −13
3x − 4y = −8

(4, 1)
(−4, 1)
(4, −1)
(−4, −1)

Answers

Answer for Question (1):

The system of equations: x+3y=6

2x-y=10

Solve the first equation x+3y=6 for y:

Subtracting x on both sides,

x+3y-x=6-x

3y=6-x

Now dividing 3 on both sides, we get

y=2-x/3 = negative one third x + 2

Thus y= negative one third of x +2

Answer for question (2):

The system of equation :

5x-3y=-3 --> (1)

2x-6y=-6 -->(2)

Multiply equation (1) by 2, we get 10x-6y=6.

Subtracting (1) by (2), we get 8x=0 implies x=0.

Plug in x=0 in equation (1), 0-3y=-3

Dividing -3 on both sides,

y=-3/-3=1

So the solution of y is 1.

Answer for Question (3):

System of equation:

7x-2y=-3 (1)

14x+y=14 (2)

Multiply (2) by 2,

28x+2y=28 (3)

Adding (1) and (3), we get 35x=25

Now dividing 35 on both sides, x=25/35=5/7.

Plug in x=5/7 in equation (1), we get 5-2y=-3

-2y=-3-5

-2y=-8

Dividing -2 on both sides,

y=4

Thus the solution of this system of equation as (5/7,4).

Answer for question (4):

x + 3y = 9 ---> (1)

3x − 3y = −13 ---> (2)

Adding equation (1) and (2), we get

4x=-4

Dividing 4 on both sides,

x=-1

Plug in x=-1 in equation (1), we get

-1+3y=9

Adding 1 on both sides,

3y=9+1=10

Now dividing 3 on both sides,

y=10/3.

so the solution is (-1,10/3).

Answer for question (5):

System of equation is 4x − y = 3 (1)

7x − 9y = −2 (2)

consider the first equation 4x-y=3

Adding y on both sides, 4x=3+y

subtracting 3 on both sides, we get y=4x-3

Substitute y=4x-3 in equation (2),

7x-9(4x-3)=-2

7x-36x+27=-2

Combine the like terms,

-29x+27=2

Adding 27 on both sides,

-29x=-29

dividing -29 on both sides,

x=1

Plug in x=1 in y=4x-3,

y=4(1)-3=1

Then the solution is (1,1).

Answer:

What is the solution to the system of equations?

6 x + 2 y = 6. 7 x + 3 y = 5.

(Negative 3, 2)

(Negative 1, 6)

(2, Negative 3)

(6, Negative 1)

Step-by-step explanation:

What is the solution to the system of equations?

6 x + 2 y = 6. 7 x + 3 y = 5.

(Negative 3, 2)

(Negative 1, 6)

(2, Negative 3)

(6, Negative 1)

There are 5 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the first stand-up comedy of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?

Answers

We have to use basic combinatorics to solver his problem. We first have to determine what kind of problem this is.

Does order matter in this question? Yes it does. So it is a permutation.

Is is a permutation with repetition? No, because once a performer goes, they cannot perform again. Hence, we have defined this problem as a permutation without repetition. The formula for this kind of question is:

$(n!)/((n-r)!)$

Where n is the number of things we choose from, and p is the number of places we want to put them in.

There are 4 places for 4 performers, because 1st performer, lets call him Joe, has already taken the 1st spot. Hence, we substitute our values:

$(4!)/((4-4)!)$

= $4!$

= $24$

There are 24 different ways to schedule this performance.

Hope this helped!

Sincerely,

~Cam943, Junior Moderator

I could use some help here

Answers

Answer:

3x^3 + 6x^2

Step-by-step explanation:

2x^2 + 3x^3 + 4x^2

Combine like terms

3x^3 + (2x^2+4x^2)

3x^3 + 6x^2

Answer:

b. 6 x² + 4 x³

Step-by-step explanation:

2x ² + 3x³ + 4x²

Combine like terms, we get

2 x² + 4 x² + 3 x³

6 x² + 3 x³

option a and b both are similar.

A ball is dropped from a height of 16 feet. The ball bounces. After each bounce, the height attained by the ball is 65% of the previous height. Write an nth term formula to model the situation. What is the maximum height attained by the ball after four bounces?1.86 feet

0.24 feet

4.39 feet

2.86 feet

Answers

2.86

After the first bounce, it is 10.4 feet
after the second, it is 6.76
after the third, it is 4.39
after the fourth, it is 2.86

What survival rate in the 10th year would make the average rate of loss over the 10-year period equal to 38.0%?

Answers

Answer: 63%

Step-by-step explanation:

First find the rate of loss that would cause the average rate of loss over the 10-year period equal to 38.0%.

Assume that rate is x.

38 = (36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x) / 10

38 = (343 + x ) / 10

380 = 343 + x

x = 380 - 343

x = 37%

The survival rate is the opposite of the rate of loss which means that the survival rate is;

= 1 - rate of loss

= 1 - 37%

= 63%

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