(a) Which of the following has only one subset? (1)

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

san4es73 [151]

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: Step 1: Trying to factor by splitting the middle term

1.1 Factoring x2-5x-36

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

Step-1: Multiply the coefficient of the first term by the constant 1 • -36 = -36

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

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

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

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

2.1 A product of several terms equals zero.

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

We shall now solve each term = 0 separately

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

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : x+4 = 0

Subtract 4 from both sides of the equation :
 x = -4

Solving a Single Variable Equation :

2.3 Solve : x-9 = 0

Add 9 to both sides of the equation :
 x = 9

6 0

2 years ago

Read 2 more answers

Cooper is measuring ingredients for his special dessert. He needs a total of 70.4 mL of milk and melted butter. The recipe calls

Pavlova-9 [17]

Answer:

Cooper needs 39.8 mL milk for his recipe

Step-by-step explanation:

Let B be the quantity of butter

and

m be the quantity of milk

So according to given statement the whole mixture measures 70.4 mL while butter measures 30.6mL

so,

B+m = 70.4

30.6 + m = 70.4

m = 70.4 - 30.6

m = 39.8 mL

Cooper needs 39.8 mL milk for his recipe ..

5 0

1 year ago

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The heights of 200 adults were recorded and divided into two categories. Which two-way frequency table correctly shows the margi

Temka [501]

Answer: c

Step-by-step explanation:

C

7 0

2 years ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$