A quadratic equation is shown below:x2 − 14x + 41 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

A:Add 8 to both sides of the equation
B:Add 9 to both sides of the equation
C:Subtract 8 from both sides of the equation
D:Subtract 9 from both sides of the equation

Answers

Answer 1

Answer: Since the desired equation is a perfect square binomial, it is necessary to obtain a constant term (in the case of the given equation, 41) that is also a perfect square. To determine the perfect square needed, take the coefficient of the second term (14x) and divide it by two, then square it. It should yield "49". To obtain 49 as the constant term, we have to add 8 to both sides of the equation. Among the choices, the correct answer is A.

Answer 2

Answer:

The first correct step to write the above equation in the form id to subtract 49 from both sides of the equation

Vertex form of an equation

The standard vertex form of an equation is expressed as:

a(x − p)² = q

Given the quadratic equation x^2 − 14x + 49 = 0

The first step is to subtract the constant of the expression from both sides as shown:

Subtract 49 from both sides of the equation to have:

x^2 − 14x + 49 = 0

x^2 − 14x + 49 - 49= 0 - 49

x^2 - 14x = -49

Hence the first correct step to write the above equation in the form id to subtract 49 from both sides of the equation

Learn more on vertex form here: brainly.com/question/17987697

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10.44 is 14.4% of what number?

Answers

10.44 / 0.144 = 72.5 :)

The function y = -0.03(x - 14)^2 + 6 models the mump of a red kangaroo where x is the horizontal distance in meters and y is the vertical distance in meters for the height of the jump. What is the kangaroo's maximum height? How long is the kangaroo's jump?

Answers

From the vertex of the quadratic equation, we find that: The kangaroos maximum height is of 6 meters.

From the roots of the equation, we find that: The kangaroo's jump is 28.14 meters long.

----------------------------

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

$f(x) = ax^(2) + bx + c$

It's vertex is the point $(x_(v), y_(v))$

In which

$x_(v) = -(b)/(2a)$

$y_(v) = -(\Delta)/(4a)$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_(v)$ , and it's value is $y_(v)$ .

----------------------------

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^(2) + bx + c, a\neq0$ .

This polynomial has roots $x_(1), x_(2)$ such that $ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))$ , given by the following formulas:

$x_(1) = (-b + √(\Delta))/(2*a)$

$x_(2) = (-b - √(\Delta))/(2*a)$

$\Delta = b^(2) - 4ac$

----------------------------

The quadratic equation is:

$y = -0.03(x - 14)^2 + 6$

Placing in standard form:

$y = -0.03(x^2 - 28x + 196) + 6$

$y = -0.03x^2 + 0.84x + 0.12$

Thus, it has coefficients $a = -0.03, b = 0.84, c = 0.12$

----------------------------

The kangaroo's maximum height is the y-value of the vertex, thus:

$\Delta = b^2 - 4ac = (0.84)^2 - 4(-0.03)(0.12) = 0.72$

$y_(v) = -(\Delta)/(4a) = -(0.72)/(4(-0.03)) = 6$

The kangaroos maximum height is of 6 meters.

----------------------------

The length of the kangaroo's jump is the positive root. The roots are found at the values of x for which y = 0, thus, the solutions of the quadratic equation.

$x_(1) = (-0.84 + √(0.72))/(2(-0.03)) = -0.14$

$x_(2) = (-0.84 - √(0.72))/(2(-0.03)) = 28.14$

The kangaroo's jump is 28.14 meters long.

A similar question is given at brainly.com/question/16858635

Answer:

Kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Step-by-step explanation:

Given : $y = -0.03(x - 14)^2 + 6$

To Find : What is the kangaroo's maximum height? How long is the kangaroo's jump?

Solution:

$y = -0.03(x - 14)^2 + 6$

x is the horizontal distance in meters

y is the vertical distance in meters for the height of the jump.

Substitute y = 0

$0 = -0.03(x - 14)^2 + 6$

$0.03(x - 14)^2 = 6$

$(x - 14)^2 = (6)/(0.03)$

$(x - 14)^2 =200$

$(x - 14) =√(200)$

$(x - 14) =14.142$

$x =14.142+14$

$x =28.142$

x≈ 28 m

Now the maximum height will be attained at mid point i.e. $(28)/(2) =14$

Now substitute x= 14

$y = -0.03(14 - 14)^2 + 6$

$y = 6$

So, kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Graph: y – 3=1/2(x+2)

Answers

Simplify and get y=1/2x+4
1/2x=slope. 4= y-intercept

Thirty-five percent of 160 is ??

Answers

The answer is fifty-six

Kenneth has entered a check payment of $350.25 in his checkbook. If the old balance was $545.95, what is his latest balance? A.)$896.25
B.)$195.70
C.)$195

Answers

Answer:

The correct option is B.

Step-by-step explanation:

The old balance of kenneth's checkbook was $545.95.

Kenneth has entered a check payment of $350.25 in his checkbook.

It means the balance of checkbook is reduced by $350.25.

The latest balance of check book is

$\$545.95-\$350.25=\$195.70$

Therefore the latest balance of kenneth's check book is $195.70. Option B is correct.

Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta? A) 59/125 B) 49/100 C) 13/25 D) 56/125

Answers

NO, that answer is wrong it is not13/25

Answer: 0.472 (or in percent near 47.2%).

if you simplify 0.472 and turn it into a fraction you will get 59/125

that is the answer on plato

P(men) or P(fit) = P(men) + P(fit) = 200/500 + 60/500 = 260/500 = 13/25

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