A) No solutions, because the number under the square root symbol in the quadratic equation (b^2 - 4ac) is negative.
B) One solutions, because the number under the square root symbol in the quadratic equation (b^2 - 4ac) is equal to 0.
The number of the cups of honey has she collected will be 52 and 2/3 cups.
<h3>What are ratio and proportion?</h3>
A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Gerrie collects honey from a few beehives.
She scoops out the honey with a small jar that holds 1/3 of a cup.
Over the last two weeks, Gerrie has filled this jar 158 times.
1 small jar = 1/3 cup
But we have done this for 158 times. Then we have
158 small jar = 158 x 1/3 cups
158 small jar = 52 and 2/3 cups
More about the ratio and the proportion link is given below.
brainly.com/question/14335762
#SPJ1
C. All of the above. Both formulas represents in calculating the slope.
<u>Step-by-step explanation:</u>
The slope(m) can be identified by the formula rise over run.
i.e. 
.
Rise is how much the line gone vertically ( y-axis) from the origin.
Run is how much the line gone horizontally (x-axis) from its origin.
∴ Rise = 
And Run = 
.
⇒ 
.
Thus both equations can be used to find the slope of the line intercept.
If the points are given you can chose them yourself from the graph. Just consider any two points on the line.
i)On z, define a∗b=a−b
here aϵz
+
and bϵz
+
i.e.,a and b are positive integers
Let a=2,b=5⇒2∗5=2−5=−3
But −3 is not a positive integer
i.e., −3∈
/
z
+
hence,∗ is not a binary operation.
ii)On Q,define a∗b=ab−1
Check commutative
∗ is commutative if,a∗b=b∗a
a∗b=ab+1;a∗b=ab+1=ab+1
Since a∗b=b∗aforalla,bϵQ
∗ is commutative.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(ab+1)∗c=(ab+1)c+1=abc+c+1
a∗(b∗c)=a∗(bc+1)=a(bc+1)+1=abc+a+1
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
iii)On Q,define a∗b=
2
ab
Check commutative
∗ is commutative is a∗b=b∗a
a∗b=
2
ab
b∗a=
2
ba
=
2
ab
a∗b=b∗a∀a,bϵQ
∗ is commutativve.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=
2
(
2
ab
)∗c
=
4
abc
(a∗b)∗c=a∗(b∗c)=
2
a×
2
bc
=
4
abc
Since (a∗b)∗c=a∗(b∗c)∀a,b,cϵQ
∗ is an associative binary operation.
iv)On z
+
, define if a∗b=b∗a
a∗b=2
ab
b∗a=2
ba
=2
ab
Since a∗b=b∗a∀a,b,cϵz
+
∗ is commutative.
Check associative.
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(2
ab
)
∗
c=2
2
ab
c
a∗(b∗c)=a∗(2
ab
)=2
a2
bc
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
v)On z
+
define a∗b=a
b
a∗b=a
b
,b∗a=b
a
⇒a∗b
=b∗a
∗ is not commutative.
Check associative
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(a
b
)
∗
c=(a
b
)
c
a∗(b∗c)=a∗(2
bc
)=2
a2
bc
eg:−Leta=2,b=3 and c=4
(a∗b)
∗
c=(2∗3)
∗
4=(2
3
)
∗
4=8∗4=8
4
a∗(b∗c)=2
∗
(3∗4)=2
∗
(3
4
)=2∗81=2
81
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
vi)On R−{−1}, define a∗b=
b+1
a
Check commutative
∗ is commutative if a∗b=b∗a
a∗b=
b+1
a
b∗a=
a+1
b
Since a∗b
=b∗a
∗ is not commutatie.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(
b+1
a
)
∗
c=
c
b
a
+1
=
c(b+1)
a
a∗(b∗c)=a∗(
c+1
b
)=
c+1
b
a
=
b
a(c+1)
Since (a∗b)∗c
=a∗(b∗c)
∗ is not a associative binary operation
Answer:
Step-by-step explanation:
R = report length
R = 40 + (3/8)R + (1/3)R
3/8 = 3*3/8*3 = 9/24
1/3 = 8*1 / 3*8 = 8/34
R = 40 + (9/24)R + (8/24)R
R = 40 + (17/24)R Subtract 17/24 from the left
R-17/24 R = 40
7/24 R = 40 Multiply both sides by 24
7R = 40 * 24
7R = 960 Divide by 7
R = 960/7
R = 137.1 which breaks the rounding rule and becomes 138 because something has to be typed on page 138
