Y= -0.3× + -0.7 think that's the equation
Two solutions were found :
1. x=4
2. x= -4
Step by step solution: Step 1 :
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0 :
Step 2 :
Checking for a perfect cube :
2.1 x3+4x2-16x-64 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+4x2-16x-64
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+4x2
Group 2: -16x-64
Pull out from each group separately :
Group 1: (x+4) • (x2)
Group 2: (x+4) • (-16)
-------------------
Add up the two groups :
(x+4) • (x2-16)
Which is the desired factorization
Trying to factor as a Difference of Squares :
2.3 Factoring: x2-16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Multiplying Exponential Expressions :
2.4 Multiply (x + 4) by (x + 4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
Equation at the end of step 2 :
(x + 4)2 • (x - 4) = 0
Step 3 :
Theory - Roots of a product :
3.1 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 :
3.2 Solve : (x+4)2 = 0
(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation :
3.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Two solutions were found :
x = 4
x = -4
(Sorry the question is too long, but I hope you understand the question)
Answer:
There are 18 tours offered each day.
Step-by-step explanation:
There are a few ways to solve this problem. Since tours are offered every 1/3 hour, we can take the amount of minutes in an hour (60) and divide by 3: 60 ÷ 3 = 20minutes. So, every 20 minutes there is a tour. Since the tours are offered every 20 minutes, or three times every hour, we can take the total time the museum is open and multiply this number by 3. The amount of hours from 10am - 4pm is 6 hours. 6 hours x 3 tours/hour = 18 total tours offered each day.
Answer:
y=-1/2 x +13
Step-by-step explanation:
negative reciprocal of 2 is -.5 and then find what y intercept it would be to go through that point
y=5x+20
If you need to you can graph this in Desmos.
y is cost, 5 is price per dog, x is the number of dogs 5 and x times each other. y is total cost.
I hope this helps.
