2x2-5x-18=0
Two solutions were found :
x = -2
x = 9/2 = 4.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 5x) - 18 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-5x-18
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 2 • -18 = -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
2x2 - 9x + 4x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-9)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 9) • (x + 2) = 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.
Answer:
4 units
Step-by-step explanation:
Answer:
y = x + 5
Step-by-step explanation:
1) First, find the slope of the line 
. We can do this by setting it up in slope-intercept form, represented by the equation 
. Whatever 
or the coefficient of the x-term is will be the slope. Isolate y in the equation:
So, the slope of the given equation is 1. Parallel lines share the same slope, thus the slope of the new line will be 1 as well.
2) Now, use the point-slope formula 
to write the equation of the line in point-slope form. Substitute values for , 
, and 
in the formula.
Since is the slope, substitute 1 for it. Since and represent the x and y values of one point the line passes through, substitute the x and y values of (-6, -1) into those places as well. Then, isolate y in the resulting equation to put the equation in slope-intercept form and find the answer:
Answer:
a) The data distribution consists of ( 7 )1's (denoting a foreign student) and ( 43 )0's (denoting a student from the U.S.).
b) The population distribution consists of the x-values of the population of 12,152 full-time undergraduate students at theuniversity, ( 6 )% of which are 1's (denoting a foreign student) and ( 94 )% of which are 0's (denoting a student from the U.S.).
c) The mean is ( 0.06 )
The standard deviation is ( 0.0336 )
The sampling distribution represents the probability distribution of the ( sample ) proportion of foreign students in a random sample of ( 50 ) students. In this case, the sampling distribution is approximately normal with a mean of ( 0.06 ) and a standard deviation of ( 0.0336 )
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
One recipe for homemade playdough calls for 4 parts flour, 1 part salt, and 2 parts water. Select all of the mixtures below that are in a proportional relationship with this recipe.
A 8 cups flour, 2 cups salt, 4 cups water
B 2 cups flour, cup salt, ½ cup water
C 6 cups flour, 1 cups salt, 3 cups water
D 10 cups flour, 1 cup salt, 2 cups water
