MATHEMATICS HIGH SCHOOL

The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring.What is the constant of the quadratic expression in this equation?

x2 + x + ___ = 0

Answers

Answer 1

Answer:

Answer:

The product of two consecutive integers is 420:

20*21 = 420 and (-21)*(-20) = 420

What is the constant of the quadratic expression in this equation?

Any constant less or equal than 0.25

Step-by-step explanation:

The product of two consecutive integers is 420 can be expressed mathematically as follows:

x*(x+1) = 420

After applying distributive property and subtracting 420 at both sides, we get:

x^2 + x - 420 = 0

In order to factorise, we use the quadratic equation as follows:

$x = (-b \pm √(b^2-4(a)(c)))/(2(a))$

$x = (-1 \pm √(1^2-4(1)(-420)))/(2(1))$

$x = (-1 \pm √(1681))/(2)$

$x = (-1 \pm 41)/(2)$

$x_1 = (-1 + 41)/(2)$

$x_1 = 20$

$x_2 = (-1 - 41)/(2)$

$x_2 = -21$

Then, 20*21 = 420 and (-21)*(-20) = 420

A quadratic equation with the standard form has a solution to the equation: a*x^2 + b*x + c = 0 if its discriminant is greater or equal than zero. Mathematically:

b^2-4(a)(c) >= 0

Here a = 1 and b = 1; then,

1^2-4(1)(c) >= 0

-4(c) >= -1

c <= -1/-4

c <= 0.25

Answer 2

Answer: x(x + 1) = 420
x^2 + x = 420
x^2 + x + (- 420) = 0 or x^2 + x - 420 = 0

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If a number of mice living in a field triples each year. what type of function represents this pattern?A.) Exponential decay
B.) Increasing linear
C.) Exponential growth
D.) Decreasing linear

Answers

Answer:

The type of function that represents this pattern is:

Option: C)

C.) Exponential growth.

Step-by-step explanation:

It is given that the number of mice living in a field triples each year.

This means that the population of mice is increasing at a constant rate i.e. 3 each year.

So, the function that represent this pattern is a exponential growth.

Also let P(t) be the function that represents the population of mice after 't' years.

Then P(t) is modeled as:

$P(t)=3^tP_0$

where $P_0$ is the initial population of the mice.

Hence, Option: C is the correct answer.

C) Exponential Growth.

Expotential Growth for Apex

The system of inequalities below describes the relationship between Cori’s age, C, and Livy’s age, L. DOK 2C + L > 43
C - 4L < 3

Which of the following could be the ages of Cory and Livy?
Livy could be 13 years old, and Cori could be 35 years old.
Livy could be 15 years old, and Cori could be 28 years old.
Livy could be 33 years old, and Cori Could be 10 years old.
Livy could be 20 years old, and Cori could be 85 years old.

Answers

Answer:

Livy could be 13 years old, and Cori could be 35 years old.

Step-by-step explanation:

Given : The system of inequalities describes the relationship between Cori’s age, C, and Livy’s age L.

C + L > 43

C - 4L < 3

We have to determine the ages of Cory and Livy.

We will plot both the inequality in a graph.

Thus, below attachment shows the graph of the two given inequality

Let x axis represent the Cori’s age, C, and y - axis Livy’s age L.

Now we plot the given ages in the graph and those points lies in intersection will given the ages of Cori and Livy.

Thus, Only (35 , 13) lies in the intersection,

We reject other points as the lies on dotted edges of graphs.

Thus, Livy could be 13 years old, and Cori could be 35 years old.

Answer:The system of inequalities below describes the relationship between Cori’s age, C, and Livy’s age, L.

C + L > 43

C - 4L < 3

Which of the following could be the ages of Cory and Livy?

Livy could be 33 years old, and Cori Could be 10 years old.

Livy could be 15 years old, and Cori could be 28 years old.

Livy could be 13 years old, and Cori could be 35 years old.

Livy could be 20 years old, and Cori could be 85 years old.

Step-by-step explanation:

Algebra II
15 points

Answers

Answer:

B. The axis of symmetry is x=1.

F. The vertex is (1, 7).

G. The y-intercept is (0, 10).

Step-by-step explanation:

A graph of the function is helpful sorting this out.

_____

For quadratic ax² +bx +c, the axis of symmetry is x=-b/(2a). Here, that is ...

x = -(-6)/(2·3)

x = 1 . . . . axis of symmetry

This is also the x-coordinate of the vertex. The y-coordinate of the vertex can be found by evaluating the expression for this value of x:

3·1² -6·1 +10 = 7

so the vertex is (1, 7).

The y-intercept is the constant, the value of the function when x=0. Here, that is 10, so the coordinates of the y-intercept are (0, 10).

[(7−5)÷12]×2
help quick

Answers

The first step for solving this expression is to subtract the numbers in the first set of parenthesis.
(2 ÷ 12) × 2
Now write the division as a fraction.
$(2)/(12)$ × 2
Reduce the fraction with 2.
$(1)/(6)$ × 2
Finally,, reduce the fraction with 2 one last time.
$(1)/(3)$
This means that the correct answer to your question is $(1)/(3)$ .
Let me know if you have any further questions.
:)

your answer would be 12

What is the equation of the line with a slope of -1/2 that passses through the points (6,6)?

Answers

m = slope

Lets put this in point slope form, and slope intercept form.

y - 6 = -1/2(x - 6)
y - 6 = -1/2x + 3
+ 6 + 6

y = -1/2x + 9

Answer: y = -1/2x + 9

Please try to help thanks