For Exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form ( A x + B y = C ) with no fractional coefficients. (See Examples 3-4). Passes through ( 6 , 8 ) and is parallel to the line defined by 3 x = 7 y + 5 .
For Exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form ( A x + B y = C ) with no fractional coefficients. (See Examples 3-4). Passes through ( 6 , 8 ) and is parallel to the line defined by 3 x = 7 y + 5 .
Solution Summary: The author calculates the equation of the line that passes through (6,8) and is parallel to 3x=7y+5 in slope-intercept form and standard form.
For Exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form
(
A
x
+
B
y
=
C
)
with no fractional coefficients. (See Examples 3-4).
Passes through
(
6
,
8
)
and is parallel to the line defined by
3
x
=
7
y
+
5
.
T. Determine the least common
denominator and the domain for the
2x-3
10
problem:
+
x²+6x+8
x²+x-12
3
2x
2. Add:
+
Simplify and
5x+10 x²-2x-8
state the domain.
7
3. Add/Subtract:
x+2 1
+
x+6
2x+2 4
Simplify and state the domain.
x+1
4
4. Subtract:
-
Simplify
3x-3
x²-3x+2
and state the domain.
1
15
3x-5
5. Add/Subtract:
+
2
2x-14
x²-7x
Simplify and state the domain.
Q.1) Classify the following statements as a true or false statements:
Q
a. A simple ring R is simple as a right R-module.
b. Every ideal of ZZ is small ideal.
very den to is lovaginz
c. A nontrivial direct summand of a module cannot be large or small submodule.
d. The sum of a finite family of small submodules of a module M is small in M.
e. The direct product of a finite family of projective modules is projective
f. The sum of a finite family of large submodules of a module M is large in M.
g. Zz contains no minimal submodules.
h. Qz has no minimal and no maximal submodules.
i. Every divisible Z-module is injective.
j. Every projective module is a free module.
a homomorp
cements
Q.4) Give an example and explain your claim in each case:
a) A module M which has a largest proper submodule, is directly indecomposable.
b) A free subset of a module.
c) A finite free module.
d) A module contains no a direct summand.
e) A short split exact sequence of modules.
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