MATHEMATICS HIGH SCHOOL

Which expression gives the solutions of -5+2x^2=-6x

Answers

Answer 1

Answer:

Answer:

The solutions are

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

Step-by-step explanation:

we have

$-5+2x^(2) =-6x$

rewrite the quadratic equation

$2x^(2)+6x-5=0$

The formula to solve a quadratic equation of the form $ax^(2) +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}$

in this problem we have

$2x^(2)+6x-5=0$

$a=2\nb=6\nc=-5$

substitute in the formula

$x=\frac{-6(+/-)\sqrt{6^(2)-4(2)(-5)}} {2(2)}$

$x=\frac{-6(+/-)√(76)} {4}$

$x=\frac{-6(+/-)2√(19)} {4}$

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

Answer 2

Answer: -5 + 2x² = -6x
rearrange the equation to the form ax² + bx + c = 0

=> 2x² + 6x - 5

use the quadratic formula to solve for the value(s) of x $-b ± \sqrt{ (b^(2) - 4ac)/(2a) }$

=> $-6 ± \sqrt{ (6^(2) - 4(2)(-5))/(2(2)) }$

=> $-6 ± \sqrt{ (36 - (-40))/(4) }$

=> $-6 ± \sqrt{ (76)/(4) }$

∴ x = $-6 + √( 19) }$ OR x = $-6 - √(19)$

x = - 1.64 ; x = - 10.36

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Help ????????please need help
CAN ANYONE HELP ME PLEASE??

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.

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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

PLEASE PLEASE PLEASE HURRY!Which is the best strategy to use to solve this problem?

Mr. Jackson wants to build a pool in his backyard. He plans to put a safety fence around the rectangular pool area that has an area of 400 square feet. He wants to use as little fence material as possible.

What are the dimensions Mr. Jackson should use for his rectangular pool area?

A.
Make a list.

Create a list of all possible whole-number combinations of length and width that would equal an area of 400 square feet. Then start calculating the perimeter of each rectangle. Look for a pattern to decrease the number of calculations you have to make.

B.
Write a number sentence.

Use a number sentence to calculate the area of a rectangle. Use guess and check to find two numbers that when multiplied will give a product of 400.

C.
Use objects.

Arrange 400 square tiles in different patterns until you get a rectangular shape. Count the number of tiles on the perimeter of the shape.

Answers

I believe it might be A or C. Not really sure

What is the 10th term in the pattern with the formula 5n + 100?

Answers

easy
first term is n=1
so 10th term is n=10

5(10)+100=50+100=150

150 is 10th term

Solve mathematics question: In photo:) Second:)

Answers

Hello,

Answer D

A Slopes :5/8,12/5==> no product is not -1

B:slopes: -1/2,3 no

C:slopes:2,-1/3 no

D:slopes:-3/2,2/3 Yes product=-1

Answer:

The answer is D

Step-by-step explanation:

Find the value of F(5) for each function.

f(a) = 3(a + 2) - 1

Answers

Answer:

Step-by-step explanation:

first plug it in, then solve. Step by step:

3(5 + 2) - 1

3(7) - 1

21 - 1

What is the product of 6x – y and 2x – y + 2?A=8x2 – 4xy + 12x + y2 – 2y
B=12x2 – 8xy + 12x + y2 – 2y
C=8x2 + 4xy + 4x + y2 – 2y
D=12x2 + 8xy + 4x + y2 + 2y

Answers

Answer:

Option (B) is correct.

The product of 6x – y and 2x – y + 2 is $12x^2-8xy+12x+y^2-2y$

Step-by-step explanation:

Consider the given expressions 6x – y and 2x – y + 2

We have to find the product of the above two given expressions,

$(6x-y)(2x-y+2)$

multiply first term of first expression by each term of second expression and similarly second term of first expression by each term of second expression

$\Rightarrow 6x(2x-y+2)-y(2x-y+2)$

On solving, we get,

$\Rightarrow 12x^2-6xy+12x-2xy+y^2-2y$

Solving further by combining like term, we get,

$\Rightarrow 12x^2-8xy+12x+y^2-2y$

Thus, The product of 6x – y and 2x – y + 2 is $12x^2-8xy+12x+y^2-2y$

Hence, option (B) is correct.

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