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Lesechka [4]
3 years ago
11

Let ​ f(x)=x2+5x−36 ​. Enter the x-intercepts of the quadratic function in the boxes.

Mathematics
2 answers:
san4es73 [151]3 years ago
6 0
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-5*x-(36)=0 

Step by step solution:<span> Step 1:</span> Trying to factor by splitting the middle term

<span> 1.1 </span>    Factoring <span> x2-5x-36</span> 

The first term is, <span> <span>x2</span> </span> its coefficient is 1.
The middle term is, <span> -5x </span> its coefficient is  - 5.
The last term, "the constant", is <span> -36 </span>

Step-1: Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -36 = -36</span> 

Step-2: Find two factors of  -36  whose sum equals the coefficient of the middle term, which is - 5.

<span><span>     -36   +   1   =   -35</span><span>     -18   +   2   =   -16</span><span>     -12   +   3   =   -9</span><span>     -9   +   4   =   -5   That's it</span></span>


Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4 
                     <span>x2 - 9x</span> + 4x - 36

Step-4: Add up the first 2 terms, pulling out like factors :
                    x • (x-9)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-9)
Step-5: Add up the four terms of step 4 :
                    (x+4)  •  (x-9)
             Which is the desired factorization

<span>Equation at the end of step  1  :</span> (x + 4) • (x - 9) = 0 <span>Step  2  :</span>Theory - Roots of a product :

<span> 2.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 2.2 </span>     Solve  :    x+4 = 0<span> 

 </span>Subtract  4  from both sides of the equation :<span> 
 </span>                     x = -4 

Solving a Single Variable Equation :

<span> 2.3 </span>     Solve  :    x-9 = 0<span> 

 </span>Add  9  to both sides of the equation :<span> 
 </span>                     x = 9 

Nezavi [6.7K]3 years ago
3 0

Answer:

x=-9\text{ or }x=4

Step-by-step explanation:

We have been given a function and we are asked to find the x-intercept of our given function.

To find the x-intercepts of our given function we will equate our function formula with 0.

x^2+5x-36=0  

Now let us factor out our given quadratic equation by splitting the middle term.

x^2+9x-4x-36=0

x(x+9)-4(x+9)=0

(x+9)(x-4)=0

(x+9)=0\text{ or }(x-4)=0

x+9-9=0-9\text{ or }x-4+4=0+4

x=-9\text{ or }x=4

Therefore, the x-intercepts of our given quadratic functions are x=-9\text{ or }x=4.

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A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular
kvasek [131]

Answer:

14 bags

Step-by-step explanation:

Dimension of lawn : 230 feet by 180 feet

area of rectangle is given by length * width

Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet

Given that one bag of fertilizer covers 3000 square feet of lawn.

Thus , to find no. of bags required to cover whole lawn will be

total area of lawn/area which one bag of  fertilizer covers

no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet

    = 13.8 bags.

As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.

8 0
3 years ago
Please help!!!
Ratling [72]

x = 3

2x + y - z = 3 → (1)

- x + y + 2z = 0 → (2)

3x + 2y + z = 9 → (3)

we require to eliminate the y and z terms from the equations

(1) + (3) : 5x + 3y = 12 → (4)

multiply (1) by 2

4x +2y - 2z = 6 → (5)

(2) + (5) : 3x + 3y = 6 → (6)

(4) - (6) : 2x = 6 ⇒ x = 3


8 0
3 years ago
Name the type of transformation that maps the pre-image, ABC, to the image, A'B'C'. show your work​
AleksAgata [21]

Answer:

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Step-by-step explanation:

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2 years ago
What is the perimeter?
Tema [17]
To find the perimeter, add all sides on the border of the shape.

In this case, don’t worry about the 15 feet inside.

This will be 11 + 16 + 16 + 6 = 49 ft.

Please give brainliest if you can!

Hope this helps! :)
6 0
3 years ago
Answer this for 99 points<br><br> 300 x 200 x 1000^ 30
klemol [59]
The answer is 6e+94 

Hope this helps!!!
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